Behavioral Economics Workbench

A working study companion for Behavioral Economics (行为经济学), built from the six lecture decks supplied so far — Introduction, Choice under Certainty, Belief, Risk, Reference-Dependent Preferences and Gender — and rearranged so that the models come first and the definitions can be moved rather than only read. The course is taught by Lu Yunfeng at Nanjing University.

Lectures 1–6 delivered · 273 slides Thirteen interactive models Graded self-checks every lecture Installable · works offline

How this workbench is organised

the same five blocks in every lecture

1 · Concept Map

How the lecture's ideas build on one another, drawn as a chain rather than a list. Where a model is answering an earlier one, the arrow says so.

2 · Core Content

Explanatory prose around the slides, with the lecture's own experiments taken apart and the technical definitions stated exactly as the deck states them.

3 · Model Labs

Thirteen figures you can drive. Where a lecture slide only reports a result, the lab lets you reproduce it, break it, and see which parameter is doing the work.

4 · Summary Sheet

The definitions, formulas and headline numbers of the lecture on one screen, in the order the lecture introduced them.

5 · Self-Check

Graded multiple choice with a written explanation for both the right and the wrong answer, plus reveal-style problems where the working matters more than the answer. Progress is kept per lecture.

Shishuo xinyu cases

All six lectures are threaded with stories from 《世说新语》. Each is kept as a case box beside the concept it illustrates, because the mapping from the story to the model is the point.

Flagged, not fixed

Where a slide is loose — a sample size that covers two different experiments, a result quoted without its numbers — the workbench says so in place instead of quietly tidying it.

Install it

Open the site on a phone and use “Add to Home Screen”. It then opens full-screen with no browser chrome and works with no network at all — including all thirteen figures.

The thirteen models

each one attached to the lecture that needs it

Model 1

The 1979 two-question experiment

Answer Problems 11 and 12 yourself, then see why they are the same question.
Compares your pair of answers against the published 1979 marginals.
The experiment every later lecture is built on.

Lecture 1

Model 2

Prospect theory

Drive α, λ and γ and watch the value function and the weighting function change shape.
Prices a 50/50 gamble and reports its certainty equivalent.
Explains why the Model 1 answers came out asymmetric.

Lecture 1

Model 3

The weak axiom, interactively

Set a choice function on four budgets and let the model hunt for a violation.
Links the abstract definition to Sen's Property α.
One preset is exactly the decoy pattern the lecture ends with.

Lecture 2

Model 4

The endowment effect

A mug market with 22 owners and 22 non-owners.
At λ = 1 it clears at exactly the 11 mugs neoclassical theory predicts.
Raises λ and the traded quantity collapses.

Lecture 2

Model 5

Decoy and compromise

The beer and battery experiments in attribute space.
Switch the third option on and off and watch the shares move.
Two different mechanisms, both violations of IIA.

Lecture 2

Model 6

Defaults and the status quo

The eleven-country organ-donation chart, from the slide.
A two-parameter model of what a default actually does.
Reproduces most of a 96-point international spread.

Lecture 2

Model 7

What a positive test means

1,000 people, one square each, coloured by test result and true status.
Move prevalence, sensitivity and the false-positive rate.
Default: Eddy's screening example, where 9 of 108 positives are real.

Lecture 3

Model 8

When does the crowd cancel?

Galton's ox, simulated: judges with independent noise and a shared bias.
More judges average out the noise, not the bias.
Shows exactly which of the slide's three conditions is doing the work.

Lecture 3

Model 9

The price of the St Petersburg game

Truncated expected value grows with the number of tosses; the certainty equivalent need not.
Curvature is the whole repair: at α = 1 the paradox returns.
Links the log-utility benchmark ($4) to the general power function.

Lecture 4

Model 10

Cumulative prospect theory on one die

Tversky & Kahneman's (1992) six-outcome example, with the slide's equation.
Bars are cumulative decision weights against the objective 1/6.
Set α, λ, γ and δ; at the 1992 estimates the loss branch dominates.

Lecture 4

Model 11

When is “I'll buy it” self-fulfilling?

The shopping problem from Kőszegi–Rabin: shoes, a price, and two dimensions of consumption.
Move the price and watch the unique-Buy, multiple-PE and unique-Not-Buy regions change.
The preferred equilibrium still follows the neoclassical rule — the interesting part is the band in between.

Lecture 5

Model 12

Bunching at the fixed payment

Marginal benefit is a step: high below f/w, low above it.
Raise the fixed payment and the high-return region lengthens.
When the two branches sit on opposite sides of the kink, the optimum is the kink itself.

Lecture 5

Model 13

Piece rate or tournament?

Task 3 of Niederle & Vesterlund in one decision.
Set your expected score, subjective win probability and taste for competing.
The risk-neutral break-even is exactly 0.25 for a four-person group.

Lecture 6

What the course covers

from the topic slide of Lecture 1

The course splits into three parts. Individual decision making is where Lectures 1–5 sit: what a rational choice is, the six documented ways actual choices depart from it, how beliefs are formed, how risk is valued, and how reference points are formed and updated. Strategic decision making takes the same questions into games, where what you should do depends on what you believe others will do. Application carries both into gender, culture and policy — Lecture 6 is the gender application.

Part I

Individual decision making

Rationality · what the standard model assumes
Beliefs · heuristics, biases, overconfidence
Risk · prospect theory
Reference points · Kőszegi–Rabin, effort
Time · present bias, discounting

Lectures 1–5 here

Part II

Strategic decision making

Others · social preferences, inequality aversion
Games · level-k, quantal response equilibrium
Experimental markets and learning

Not yet posted

Part III

Application

Gender · the seven factors, tournaments, culture
Culture
Nudging and policy design

Lecture 6 here

Assessment and contact

as stated on the last slides of Lecture 1

Component	Weight	Detail
Classroom performance	20%	Discussion participation and presentation
Two problem sets	20%	Two sets across the semester
Final exam	60%	Everything in the lectures and the paper list

✉ Where things are posted

Email luyunfeng@nju.edu.cn. The QQ discussion group is 1085521262. The course runs an online double-auction experiment at veconlab.com; the session name used in the lecture was yfnj21.

Your progress

stored on this device only

Progress lives in this browser's local storage under the key be-progress-v1. Clearing site data or switching browser resets it, and it does not travel between the computer and the phone.

Lecture 1

Introduction

Source: lecture 1 introduction 2026.pptx — 47 slides Lu Yunfeng · Department of Economics Runs the opening classroom experiment

This lecture does three things. It runs an experiment on you in the first five minutes. It defines what behavioral economics is not — not a claim that people are irrational, not a rejection of the standard model — and states the three properties a departure has to have before it counts as a finding. And it sketches eighty years of history to explain how economics came to lose its psychological content in the first place, so that the project of putting it back can be seen for what it is.

The examinable core is the vocabulary: the three pillars of the neoclassical benchmark, the three properties of a behavioral finding, and the four currents that converged in the second half of the twentieth century. The opening experiment is worth doing rather than reading — it is the cleanest single demonstration in the course, and the two questions are the same question.

Concept map

how the lecture builds

ExperimentTwo questions that are one question. Most people answer them inconsistently.

a departure has to earn the name

SystematicDepartures share a direction; they are not noise.

PredictableThe direction can be stated before the experiment.

FormalizableStill utility maximisation — a different utility function.

measured against a benchmark

The three pillarsBelief · Preference · Equilibrium. Behavioral economics replaces their assumptions one at a time.

which is why the history matters

Economics and psychology were one subjectSmith, Bentham, Fisher, Keynes — up to the 1930s.

Then they separatedPareto, revealed preference, the as-if defence. A successful methodological retreat.

and why the reunion took four separate movements

Bounded rationalitySimon · satisficing

Cognitive biasKahneman & Tversky · heuristics

Experimental marketsVernon Smith · institutions can correct bias

NudgingThaler · RCTs in government

and how any of it gets tested

Lab experimentControl, but a selected subject pool

Field experimentArtefactual · framed · natural

Field dataIV · DID · RD

Structural estimationEstimate the parameters, then run counterfactuals

The experiment the lecture opens with

slides 2–5

The lecture begins with two questions put to the room, answered on paper before anyone sees the second one. They are Problems 11 and 12 of Kahneman and Tversky (1979), and they are the founding demonstration of the whole field: two decisions that are identical in final-wealth terms and that most people answer differently.

Model 1

The two-question experiment

Answer both, then read the reveal. The point is not which answer you gave but whether the two answers agree.

Why the two questions are the same question

Each question hands you a sum of money first, then offers a choice. Put the grant and the outcome together and the two problems have the same four terminal states:

Question	The gamble pays	The sure option pays
Q1 — grant ¥1,000, then choose	¥2,000 with p = 0.5, ¥1,000 with p = 0.5	¥1,500
Q2 — grant ¥2,000, then choose	¥2,000 with p = 0.5, ¥1,000 with p = 0.5	¥1,500

Anyone who takes the gamble in Q1 must take it in Q2. Kahneman and Tversky found that most people take the sure option in Q1 and the gamble in Q2 — which is exactly what the classroom experiment tends to reproduce.

→ The mechanism: the reference point moves

In Q1 the grant is the reference point, so the risky branch is read as a gain of ¥1,000 against a certain gain of ¥500 — and people avoid the risk. In Q2 the larger grant is the reference point, so the same two terminal states are read as a loss of ¥1,000 against a certain loss of ¥500 — and people take the risk.

Nothing about the outcomes changed. What changed is which side of the reference point they sit on. This is the isolation effect 隔离效应, and it is the reason Lecture 1 hands off to prospect theory.

! A figure on the slide that needs care

The comparison slide asks the class to fill in its own percentages and compare them against “the 68 subjects of 1979”. In the 1979 paper the two problems were run on different samples: Problem 11 on N = 70, Problem 12 on N = 68. The single N on the slide is Problem 12's. The published marginals are 84% choosing the sure option in Problem 11 and 69% choosing the gamble in Problem 12.

Worked What the 1979 marginals imply about the modal answer

Suppose the two answers were given independently. Then the share of subjects who took the sure option in Problem 11 and the gamble in Problem 12 is the product of the two marginals.

Share choosing B1 (the sure option) in Problem 11: 0.84
Share choosing the gamble in Problem 12 — i.e. rejecting the sure loss: 0.69
Product, under independence: 0.84 × 0.69 = 0.5796
As a percentage of the two samples: 58.0%

So the inconsistent pair — sure in Q1, gamble in Q2 — is the modal answer, at roughly 58% of respondents, while the consistent answer the final-wealth argument requires is close to a minority position.

The independence assumption is doing real work in that multiplication. The 1979 paper reports the two problems separately and never cross-tabulates them, so the joint share is a reconstruction, not a published number.

What behavioral economics is

slides 6–8

The lecture's definition is deliberately modest, and worth reading closely:

Using psychological evidence on how people actually decide to improve the behavioral assumptions of economics — not to overturn it, but to predict better.

A departure from the standard model only becomes a behavioral finding if it has all three of these properties. This is the test the course will apply all semester.

Systematic 系统的

Departures from the standard model share a common direction rather than being random noise — the same population departs in the same direction at different times.

Predictable 可预测的

Theory can state the direction and rough magnitude of a departure before the experiment is run. This is what separates it from after-the-fact narrative explanation.

Formalizable 可模型化的

The language remains utility maximisation: we replace the utility function, the discount function or the specification of beliefs, rather than abandoning the analytical toolkit.

Why the third one matters most 为什么第三条最关键

A finding that cannot be written into a model cannot generate a new prediction, and a claim that generates no new prediction cannot be refuted. All three properties are in service of being refutable.

The benchmark: the three pillars

Everything behavioral economics does is defined against this. Learn it as three columns, because the lecture's next slide replaces them column by column.

Pillar	What the standard model assumes
Belief 信念	Probabilistic judgment obeys the laws of statistics · new information is incorporated by Bayes' rule · beliefs about others' strategies are correct
Preference 偏好	Self-interest · expected utility, including the independence axiom · time consistency, i.e. exponential discounting
Equilibrium 均衡	Everyone is maximising · beliefs and strategies are mutually consistent · Nash equilibrium

The lecture's own defence of this benchmark: its predictions are sharp and falsifiable, which is a virtue — a model that cannot be wrong cannot be corrected either.

And what replaces them, one pillar at a time

Pillar	The behavioral replacement	Introduced
Belief	Heuristics and biases · biased and motivated beliefs · overconfidence	Week 6
Preference	Social preferences (inequality aversion) · prospect theory (reference points, loss aversion) · quasi-hyperbolic discounting (present bias)	Weeks 4–5, 7+
Equilibrium	Limited strategic thinking (level-k) · quantal response equilibrium · learning models	Weeks 14+

The weeks are read off the lecture's own topic slide and its cross-references; they are the instructor's sequencing, not a fixed syllabus.

Model 2

Prospect theory: the value function and the weighting function

This is the replacement for expected utility, and it is what makes the opening experiment come out the way it does. Drive the three parameters and watch both functions move.

→ How Model 2 explains Model 1

Put the gamble from Question 1 into the prospect value: a 50% chance of gaining ¥1,000 and a 50% chance of nothing. Under the default parameters the value of that gamble comes out well below the value of a certain ¥500, so the sure option wins — and the model predicts it without being told about the reference point, because the value function is kinked at zero and steeper below it.

Now re-code the same two branches as losses, which is what Question 2's larger grant does. The kink works the other way, the certain loss looks worse than the gamble, and the risk is taken. The asymmetry between the two questions is not a separate finding — it is the shape of one curve.

“Behavioral economics is not saying that people are irrational”

slide 9

The slide puts that sentence in quotation marks and then spends three points qualifying it. The qualifications are the examinable content.

1 · The departures are systematic

Because they have a direction and a regularity, they can be written into a model, used to make predictions, and refuted by data. Random error could not be any of those things.

2 · Markets correct some biases and amplify others

Vernon Smith's experimental markets converge to the competitive equilibrium. In an asset bubble, the same biases are amplified instead of washed out.

3 · Which case obtains is an empirical question

What the course trains is the method for making that judgement, not a ready-made position on whether markets work.

The question therefore always comes in two steps

Does the bias exist at the individual level? And under which institutions is it amplified, and under which is it eliminated? Point 2 is what makes the second step non-trivial — individual bias does not mechanically produce market-level deviation.

? The tension to hold on to

Point 1 says departures are systematic and therefore modellable. Point 2 says the market-level consequence is not determined by the individual-level bias. Those are consistent, and the lecture's framing depends on keeping them apart: behavioral economics is a claim about individual decision rules, and it is agnostic in advance about what aggregating them produces.

Case · Wang Rong, or: do preferences change?

slides 11–14

Before the history, the lecture puts a problem from fourth-century China next to the modern one. Wang Rong (王戎), one of the Seven Sages of the Bamboo Grove, appears in 《世说新语》 as two different people.

The child 《世说新语 · 雅量》

王戎七岁尝与诸小儿游，见道旁李树多子，折枝，诸儿竞走取之。唯戎不动。人问之，答曰：“树在道边而多子，此必苦李。”取之信然。

Aged seven, Wang Rong declines to pick plums from a roadside tree heavy with fruit: a tree by a road that still has fruit must bear bitter plums. He was right. The reasoning is impeccable — this is a seven-year-old running a selection argument.

The old man 《世说新语 · 俭啬》

王戎有好李，卖之，恐人得其种，恒钻其核。

王戎俭吝，其从子婚，与一单衣，后更责之。

Wang Rong owned good plums; he sold them and, to stop buyers from growing their own, drilled out the pits. He gave his nephew a single robe for a wedding and then asked for it back. And yet, in 《德行》, he refuses a fortune in condolence money after his father's death.

The slide's own reading is blunt: 王戎似乎变成了另一个人，前后行为不一致 — Wang Rong seems to have become a different person; his behaviour before and after is inconsistent. Behavioral economics, the slide says, holds that preferences change 偏好会发生改变: clever and generous when young, a miser by the end.

? The question the slide leaves open

How would the neoclassical model explain it? The standard model holds preferences fixed — a stable ordering over outcomes — and puts all the movement in constraints and information. So it has to say that what changed was not Wang Rong's taste for money but something else: his wealth, his expectations of the future, or his beliefs about what others would do with his plums. The behaviorist reading says the preference ordering itself moved.

These are different claims and they are not distinguished by the story. That is the point of putting the story next to the experiment: the experiment is what tells them apart.

☰ Why the deck uses 《世说新语》 at all

The lecture's own statement of method: a theory abstracted from the real world can be verified in the laboratory, and it can also be found in medieval China — the behaviour of the people in 《世说新语》 may be consistent with behavioral economics' insights.

A caution worth stating: a story that can be read as a preference reversal is not evidence of one. Every story below should be read the same way — as an illustration of a mechanism that the experiments establish, not as a substitute for them.

About the book itself

Title	《世说新语》 · A New Account of Tales of the World
Author · annotator	刘义庆著，刘孝标注
Structure	36 sections · 1133 anecdotes · over 1,000 people. Organised by the nature of the event, not by biography — 德行、言语、文学、政事、雅量、捷悟、企羡、贤媛、俭啬、纰漏 and so on.
Why the structure matters	Because it is thematic rather than chronological, one person's behaviour can be read across sections — which is exactly what makes the Wang Rong comparison possible. A conventional biography would have smoothed it over.

宗白华's assessment, quoted on the slide: the late Han–Wei–Six Dynasties was the most politically chaotic and socially miserable period in Chinese history, and yet the most free and liberated in spirit, the richest in wisdom and in passion — and therefore the most artistic.

The Nanjing connection 《世说新语 · 言语》

过江诸人，每至美日，辄相邀新亭，藉卉饮宴。周侯坐而叹曰：“风景不殊，正自有山河之异！”皆相视流泪。唯王丞相愀然变色曰：“当共戮力王室，克复神州，何至作楚囚相对？”

The émigré gentry, having crossed the Yangtze, would gather at Xinting on fine days. Zhou Yi sighed that the scenery was unchanged while the land was not, and everyone wept — until Wang Dao turned on them: we should be working to recover the north, not sitting here like prisoners. The gathering place and the court it defended are both in Nanjing, where these lectures are being given.

History of ideas

slides 15–17

I · For a long time, economics and psychology were one subject

1759

Adam Smith
The Theory of Moral Sentiments

1789

Bentham
on utility

1930

Fisher
on “impatience”

1936

Keynes
animal spirits

Four moments at which the psychological content was still inside the economics

1759 · Smith	Sympathy, a sense of fairness, social norms and self-command — seventeen years before The Wealth of Nations. The author of the invisible hand also wrote the book on moral sentiment, and the lecture's point is that this is not a contradiction to be explained away.
1789 · Bentham	Utility was defined directly as the psychological quantity of pain and pleasure, a sensation open to introspection. Note how far this is from the modern definition, in which utility is whatever a preference ordering can be represented by.
1930 · Fisher	The first systematic discussion of intertemporal choice, explicitly about self-control and foresight — the subject of his analysis was a person, not a discount factor.
1936 · Keynes	Animal spirits, and the beauty contest: prices depend on the market's expectations of others' expectations. The guessing game in week 14 is its experimental version.

II · The birth of homo economicus — a successful methodological retreat

Move	What it did
Pareto	At the end of the nineteenth century he argued that economics should separate from psychology: study choice, not desire.
Revealed preference	Samuelson grounded preference entirely in observable choice, clearing psychological content out of the theory.
The as-if defence	Friedman: assumptions need not be realistic so long as predictions are accurate — a defence of the highly simplified rational agent.

→ Why the lecture calls this a successful retreat

Economics gained rigorous analytical tools and a common language. That is not a loss to be mourned. What behavioral economics does is bring the psychological content back in a testable form — it does not ask for the tools to be given up.

This is the same point as the third property of a behavioral finding. The toolkit stays; the assumptions get replaced.

III · Four currents converge

#	Current	Principal	Contribution
1	Bounded rationality	Simon	People do not maximise; they satisfice
2	Cognitive bias	Kahneman & Tversky	Departures are systematic, identifiable and classifiable
3	Experimental markets	Vernon Smith	Bringing market institutions into the laboratory to ask when they work
4	Nudging and policy	Thaler, and RCTs	Turning findings into interventions that can be implemented and evaluated

The four currents, one at a time

slides 18–29

I · Bounded rationality — Simon

“ The claim, in Simon's words

“There is a complete lack of evidence that, in actual human choice situations of any complexity, these computations can be, or are in fact, performed.”

Notice what Simon is and is not claiming. He is not saying people choose badly. He is saying the computation the standard model demands exceeds what people can actually do — so the model cannot be describing the process, whatever it says about the outcome.

Satisficing 满意化

Do not search the whole option set; stop once an acceptable level is reached.

Three constraints on rationality

Incomplete information · limited computational capacity · costly time.

Implication for models

Replace “maximisation” with “stop when search costs bite”, and the predictions change.

The tell

This is the first current in the lecture that changes the process rather than the objective. Prospect theory will change the objective; Simon changes the procedure.

Simon's memoir Models of My Life is on the slide, and the three books below are the lecture's recommended route into the field — none of them is a textbook, and the slide asks you to finish at least one this semester.

Thinking, Fast and Slow	Daniel Kahneman	The two-systems framework; the spine of week 6
Misbehaving	Richard Thaler	The fullest narrative history of the field
The Undoing Project	Michael Lewis	The collaboration of Kahneman and Tversky, and its breakdown

II · Cognitive bias — Kahneman and Tversky

Judgment relies on a few heuristics — representativeness, availability, anchoring — which work in most situations and necessarily produce bias in particular ones. “Necessarily” is the load-bearing word: a shortcut that always worked would not be a bias.

Richard Thaler (Nobel 2017) carries the same programme into policy, from mental accounting to nudging — the main figure behind behavioral economics entering the world of government.

III · Experimental markets — Vernon Smith

In a double auction, each subject knows only their own private valuation. Nobody knows where the supply and demand curves lie — there is no posted price and no auctioneer reading out excess demand. Yet after a few rounds of trading, prices converge to the competitive equilibrium price and quantities to the equilibrium quantity.

! Why this matters for the whole course

Behavioral economics is most easily misread as “markets do not work”. Smith's results are a reminder that bias at the individual level need not translate into price deviations at the market level. Whether an institution corrects bias is an empirical question, and it has different answers for different institutions.

Smith shared the 2002 Nobel Prize with Kahneman — experimental method and psychological evidence were recognised together, which is the lecture's way of saying the two halves belong to one programme.

The lecture's own classroom version of this is the online double auction at veconlab.com: 4 rounds of transactions, 79 participants in the session whose results are shown. Two treatments were run and their transaction prices converged to different levels — the blue series settling near $6 and the red near $7, against a supply–demand crossing at a little under $7.

Those two levels are read off the rendered results chart on slide 46 — the chart is an image, not text, and its price axis is gridded at $1 intervals, so the figures are approximate to about half a dollar. The precise treatment definition is not stated on the slide.

IV · Nudging and policy — Thaler, and the RCT

Case	What changed	Effect
The UK nudge unit	The Behavioural Insights Team, founded 2010, applied randomised controlled trials to everyday administration: tax collection letters, organ donation registration, employment services.	—
The neighbours on the electricity bill	Adding a comparison with neighbours' consumption to the bill.	≈ 2% less household electricity Allcott (2011)
Interventions in developing countries	From the pricing of bed nets to small incentives for vaccination, RCTs became the standard tool for evaluating anti-poverty policy (Banerjee & Duflo).	—

! The lecture's own caution on the electricity result

Two per cent is enough to justify a rollout, but a limited effect that should not be overstated. A statistically robust and policy-relevant effect can still be a small one, and the slide says so rather than letting the number speak for itself.

One change of default, inside an app you use every day

The clearest case on the slides is a food-delivery platform that changed disposable cutlery from included by default to something the user has to tick a box for, paired with a small green-points reward.

Case Why this is anomalous

The change removed no one's options and raised no one's costs. The feasible set is unchanged and so are prices.

Under the standard model the default should not affect choice — nothing in the constraint set or the price vector moved.
The observed change in the share of “no cutlery” orders: +648%
Whether this is a bias or a correction is not settled by the size of the number. A user who simply never thought about cutlery is being helped; a user who wanted cutlery is being inconvenienced. The experiment measures the response, not the welfare.

This is the class of phenomena weeks 4–5 are devoted to, and the reason the default is described in the lecture as one of the most powerful methods of behavioral nudge.

He, Pan, Park, Sawada & Tan (2023), “Reducing single-use cutlery with green nudges: evidence from China's food-delivery industry”, Science 381(6662).

The same method, under its industry name

A/B testing is a randomised controlled trial. An engineer at Microsoft Bing proposed changing the way ad headlines were displayed. The idea was judged low priority and sat for six months. Once launched as an A/B test, search advertising revenue rose about 12% — more than 100 million dollars a year.

! The one thing the slide asks you to remember

Expert prior judgement kept the proposal on the shelf for six months; a randomised experiment overturned that judgement within days. This is exactly why the course teaches experimental method: intuition predicts behaviour far less reliably than we think.

Note the symmetry. The same argument was used against behavioral economics a few slides earlier — that our intuitions about how people decide are unreliable. It applies to the researcher's intuitions too.

Source, as cited on the slide: public reports by Kohavi and co-authors on online controlled experiments at Bing.

Empirical methods

slides 32–40

Four slides, four methods. The lecture's framing is that every one of them is a way of answering the causality question, and they differ in how much control the researcher has and how much the setting resembles the world.

Lab experiment

Design concerns

Experimental instructions · anonymity · matching protocols and reputation building · incentives · order effects · within-subjects versus between-subjects design · study, treatment, session · statistics for the experimenter: t-test and nonparametric tests.

Forms

Pen and pencil · online survey (Qualtrics, 问卷星) · z-Tree / oTree, which is based on Python.

Procedure, in order

Experimental design → IRB application → writing the programs and the instructions → subject recruitment → running the session (consent form, reading the instructions, payment) → analysing the data.

Why the IRB step is not administrative

Deception, payment and anonymity are all design variables here, not housekeeping. Changing the anonymity rule changes the behaviour you are measuring.

Field experiment

Type	Definition
Artefactual field experiment	A conventional lab experiment but with a nonstandard subject pool
Framed field experiment	Subjects know they are in the experiment
Natural field experiment	Subjects do not know they are in the experiment

The slide's own aside on this slide — “Chinese medicine? Randomised double-blind large sample experiment?” — is a rhetorical question about the standard of evidence implied by the phrase, not a fourth category.

Field data

Data sets are public surveys, micro data sets and administrative data. The empirical strategy is identification: find the natural experiment that pins down causality. The slide lists four approaches.

#	Strategy	What identifies the effect
1	Experimental ideal	Randomisation itself
2	Instrumental variable	A variable that moves the treatment but nothing else — the slide's examples are weather and government policies
3	Difference-in-differences	Control group and treatment group, before and after
4	Regression discontinuity	A threshold rule that assigns treatment

DID Real-time feedback and resource conservation

Tiefenbeck et al. (2016), Management Science. Participants: 636 one- and two-person households in Switzerland. A smart shower meter displays energy and water use in the shower itself.

Control condition — no feedback on water; only the temperature is displayed.
Real-time feedback condition — the meter shows consumption as it happens.
Real-time plus past feedback condition — consumption now, and the history alongside it.

Resource use drops by 22% upon activation of the display, and the treatment effect remains stable throughout the study (p < 0.01).

Two details from the figure's own note: the energy and water series move almost identically, with a correlation coefficient of 0.989; and the difference-in-differences design is what makes the drop attributable to the display rather than to the passage of time, since the control group's consumption drifts too.

The design shows why DID is needed rather than a simple before/after: in the figure, the control group's usage also falls across the study. Only the difference between the two paths identifies the treatment effect. Note also that “stable throughout” is a stronger and more useful result than “significant on average” — it rules out a novelty effect that decays.

Structural estimation

Assuming the economic theory is correct, use the data to estimate the value of the key parameters with statistical methods such as maximum likelihood estimation. The estimated parameters and the model are then used to do counterfactual policy analysis.

The slide's examples: risk-aversion parameters in utility models, and the cognitive hierarchy model. Both are parameters that cannot be observed directly — you recover them by asking what value would make the observed choices most likely.

→ How the four methods relate

Lab and field experiments create the variation. Field data finds variation that already exists. Structural estimation takes a model as given and asks what its parameters must have been. The first three are about identification; the fourth is about measurement, and it is the only one that can answer a question about a policy that has never been run.

Summary sheet

printable

Behavioral economics 行为经济学

Using psychological evidence on how people actually decide to improve the behavioral assumptions of economics — not to overturn it, but to predict better.

The three properties

Systematic · Predictable · Formalizable. A departure with only the first two is an anecdote; with only the first and third it is a curve fit.

The three pillars

Belief — Bayes' rule, correct beliefs about others · Preference — self-interest, expected utility, exponential discounting · Equilibrium — mutual best response, Nash.

The four currents

Simon (bounded rationality) · Kahneman & Tversky (cognitive bias) · Vernon Smith (experimental markets) · Thaler (nudging and policy).

Isolation effect 隔离效应

Choices are made relative to a reference point supplied by the framing, not over final wealth. The 1979 two-question experiment is its cleanest demonstration.

Satisficing 满意化

Stop searching once an acceptable level is reached, rather than searching the whole option set for the maximum.

Field experiments, by degree of disguise

Artefactual — lab protocol, nonstandard pool · Framed — subjects know · Natural — subjects do not know.

The four identification strategies

Experimental ideal · instrumental variable · difference-in-differences · regression discontinuity.

Key concepts

English term · 中文

Term	中文	Meaning in this lecture
Behavioral economics	行为经济学	Improving the behavioral assumptions of economics with psychological evidence, keeping the analytical toolkit.
Neoclassical benchmark	新古典基准	The three pillars — belief, preference, equilibrium — whose predictions are sharp and therefore falsifiable.
Isolation effect	隔离效应	Choices depend on the framing of the components rather than on final wealth. Problems 11 and 12 of Kahneman & Tversky (1979).
Reference point	参照点	The state against which outcomes are coded as gains or losses. The grant in each question moves it.
Bounded rationality	有限理性	Simon: the computation the standard model requires exceeds what people can perform, so the model cannot describe the process.
Satisficing	满意化	Search stops at an acceptable level rather than continuing to the maximum.
Heuristic	启发式	A judgment shortcut that works in most situations and necessarily produces bias in particular ones — representativeness, availability, anchoring.
Double auction	双向拍卖	A market institution in which buyers and sellers both post bids and offers. Prices converge to the competitive equilibrium even with no public information about the curves.
Nudge	助推	An intervention that changes behaviour without removing options or changing prices — a change of default is the standard example.
A/B test	A/B 测试	A randomised controlled trial run on a live product. The Bing headline case: about 12% more advertising revenue.
Difference-in-differences	双重差分	Comparing the change in a treatment group against the change in a control group, because the control group's path is not flat.
Structural estimation	结构估计	Recovering unobservable parameters — risk aversion, strategic depth — by maximum likelihood, then running counterfactual policy analysis with them.

Self-check

graded, with explanations

0 / 0 correct

The opening experiment

Q1Kahneman and Tversky's Problems 11 and 12 put different sums in the subject's hand before the choice. Why does that make the two problems the same problem?

Correct.Each problem is a grant plus a choice. Q1: ¥1,000 grant, then either +¥1,000/+¥0 or +¥500 — giving ¥2,000/¥1,000 or ¥1,500. Q2: ¥2,000 grant, then either −¥1,000/−¥0 or −¥500 — giving ¥1,000/¥2,000 or ¥1,500. Same four states, same probabilities.

Not quite.Work out the terminal wealths rather than reasoning about the grants in the abstract. Add each grant to each branch of each question. The probabilities are in fact identical across the two problems; what the question turns on is the amounts lining up after the grant is added.

Q2A subject takes the sure option in Q1 and the gamble in Q2. On the lecture's account, what has happened?

Correct.The grant becomes the reference point. In Q1 the sure branch is a gain of ¥500 against a possible ¥1,000 — risk is avoided. In Q2 the sure branch is a loss of ¥500 against a possible ¥1,000 loss — risk is taken. This is the isolation effect, and prospect theory is built to predict its direction.

Not quite.The stakes are the same in both questions once the grant is added — that is the whole point of the experiment. And the pattern is not undescribable: prospect theory states its direction in advance, which is what makes it a behavioral finding rather than a curiosity.

Definition and benchmark

Q3Which of these is not one of the three properties a behavioral departure must have?

Correct.The three are systematic, predictable and formalizable. Whether an intervention improves welfare is a separate question — one the lecture raises about the cutlery nudge precisely because the size of the response does not settle it.

Not quite.The slide lists exactly three: the departure has a direction, the direction can be stated before the experiment, and the departure can be written into a maximisation problem. Welfare is not on the list.

Q4Under the neoclassical benchmark, what does the Preference pillar assume?

Correct.Bayes' rule belongs to Belief; mutual consistency and universal maximisation belong to Equilibrium. The three replaceable pieces of the Preference pillar are self-interest, expected utility and exponential discounting — and those are exactly the three the behavioral column replaces with inequality aversion, prospect theory and quasi-hyperbolic discounting.

Not quite.Sort the options by pillar. Bayes' rule is a claim about belief formation; mutual consistency and universal maximisation are claims about equilibrium. Only one option lists pieces of the preference ordering itself.

History and the four currents

Q5The lecture calls the separation of economics from psychology a “successful methodological retreat”. Why successful?

Correct.The retreat bought rigour. Pareto, Samuelson's revealed preference and Friedman's as-if defence cleared psychological content out — and behavioral economics does not ask for the toolkit back, only for the assumptions to be replaced one at a time.

Not quite.Re-read the last line of that slide: the retreat succeeded, economics gained rigorous tools and a common language, and what behavioral economics does is bring the psychological content back in a testable form. The as-if defence is a defence of simplified agents, not a proof that assumptions never matter.

Q6Vernon Smith's double-auction experiments are on the slides because they complicate which claim?

Correct.In a double auction nobody knows where the curves lie, yet prices converge to the competitive equilibrium. So bias at the individual level need not show up as a price deviation — whether an institution corrects bias is an empirical question, which is why the course asks its question in two steps.

Not quite.Smith's results are not evidence that individuals are rational, nor a failed replication of anything. The convergence happens despite individual-level limits, which is why they are a warning against reading “behavioral” as “markets do not work”.

Methods

Q7Subjects are recruited at a market and do not know that anything about their visit has been manipulated. Which type of field experiment is this?

Correct.The distinguishing feature is exactly whether subjects know they are in the experiment. Framed — they know. Natural — they do not. Artefactual — a conventional lab protocol with a nonstandard pool, so the subjects know perfectly well. C and D name the same thing.

Not quite.The slide defines the three types along one dimension only: how much the subjects know. Options C and D describe each other — an artefactual experiment is a lab experiment with a nonstandard subject pool — which is your clue that neither is the answer.

Q8The Tiefenbeck study reports that resource use falls 22% when the shower display is activated, and that the effect is stable throughout. Explain why the design needs a control group, and why “stable” is a stronger claim than “significant”.

Why the control group is needed. The reported drop is a before/after comparison, and a before/after comparison confounds the treatment with everything else that changes over the study period — the season, the price of energy, the households' own habits. In the study's own figure the control group's consumption also drifts downward across the 70 showers. Only the difference between the two paths identifies the effect of the display. That is the difference-in-differences design: control group and treatment group, before and after.

Why “stable” is stronger. A significant average effect is compatible with a large immediate response that decays to nothing — a novelty effect. Because the display is an intervention that people could simply stop attending to, decay is the natural alternative hypothesis. The design has three arms precisely to test it: the third arm adds past consumption to the display, and if the effect were a short-lived novelty the two feedback arms would separate over time. Reporting that the effect holds through the study, with p < 0.01, is a claim about the whole path rather than about the mean.

The lesson the lecture is drawing. This is what “a departure has to be predictable and formalizable” buys you. “People use less water when shown their use” is not yet a finding; “the response is immediate, large, and does not decay over 70 showers” is, because a model of attention or of habit could have predicted the opposite and been refuted.

Lecture 2

Choice under Certainty

Source: lecture 2 choice under certainty.pptx — 34 slides Based on MWG Ch. 1 and Rubinstein, Lecture Notes, Ch. 1–3 Twelve slides are images, not text

The lecture has two halves that look unrelated and are not. The first half — about two thirds of the slides — builds the standard theory of choice from nothing: a preference relation, the two axioms that make it rational, a utility function that represents it, and then an entirely separate construction that starts from observed choices instead of from preferences. The second half lists six ways actual choices depart from that theory.

The connection is the weak axiom. The first half proves that a rational preference relation generates a choice structure satisfying it, and — the harder direction — that a choice structure satisfying it can be rationalised by a preference relation. The second half is a catalogue of violations. Every one of the six behaviors is a way for a real choice function to fail the weak axiom, and the lecture's experiments are designed to make the failure visible in a statistic.

Much of the technical content — every definition and the whole of the weak-axiom development — is on slides that are images rather than text. Everything quoted from them here was read off the rendered slide.

Concept map

how the lecture builds

Two routes to the same objectStart from preferences, or start from choices. The lecture develops both and then links them.

route one — the mental attitude

Preference relation ≽A binary relation on X: “at least as good as”.

Definition 1 · rationalComplete + transitive.

Definition 1aDerive strict preference > and indifference ~ from ≽.

Dutch bookWhy transitivity is not bookkeeping — intransitive preferences can be pumped for money.

and its numerical representation

Definition 2 · utility functionu represents ≽ when x ≽ y ⟺ u(x) ≥ u(y).

Proposition 1Representable ⟹ rational. Not the converse.

Non-uniquenessv = f(u) for any strictly increasing f represents the same preferences.

Finite XRational ⟹ representable, provided X is finite.

route two — the observable choice

Choice structure (2^B, C())A rule assigning a nonempty chosen set to every budget.

The weak axiomAn element chosen when y was available cannot lose to y in a smaller budget.

Sen's Property α / IIAx ∈ B ⊆ A and x ∈ C(A) ⟹ x ∈ C(B).

the link, in both directions

Proposition 2Rational ≽ ⟹ the C() it generates satisfies WA.

Definition 4 · rationaliseC(B) = C*(B, ≽) for every budget B.

Proposition 3WA + every subset up to three elements ⟹ a rational ≽ rationalises C(), and it is unique.

and then the violations

Mental accountingMoney is not fungible across accounts

Sunk costPast outlays affect current choice

FramingWording moves the choice

EndowmentWTA above WTP

Status quoThe default decides

Menu dependenceDecoy and compromise effects

The preference-based approach

slides 3–6

The lecture opens with the route that starts inside the head. Note the phrase it uses for the primitive: preferences are a mental attitude. Everything below is the standard development from MWG Chapter 1, and the deck states it with its own numbering.

Def 1 Rationality of a preference relation

≽ is a binary relation on the set of alternatives X, allowing the comparison of pairs of alternatives x, y ∈ X. Read x ≽ y as “x is at least as good as y”.

The preference relation ≽ is rational if it possesses the following two properties:

Completeness 完备性

For all x, y ∈ X, we have that x ≽ y or y ≽ x (or both).

Transitivity 传递性

For all x, y, z ∈ X, if x ≽ y and y ≽ z, then x ≽ z.

“Or both” in completeness is doing work: it is what allows indifference to be derived rather than assumed. Completeness requires a ranking to exist; it does not require it to be strict.

阮宣子 and “将无同” 《世说新语 · 文学》

阮宣子有令闻，太尉王夷甫见而问曰：“老庄与圣教同异？”对曰：“将无同。”太尉善其言，辟之为掾。世谓“三语掾”。卫玠嘲之曰：“一言可辟，何假于三？”宣子曰：“苟是天下人望，亦可无言而辟，复何假一？”遂相与为友。

Asked whether Daoism and Confucianism agree, Ruan Xuanzi answers “将无同” — something like “probably not different” — and is appointed on the strength of it. The slide's question: if “将无同” is taken as a preference relation, what is it? （注：据《晋书》与考证，应为阮瞻，而非阮修。）

The answer the definition supplies: it is a relation that declines to rank. It asserts neither x ≽ y nor y ≽ x with any confidence — which is exactly a failure of completeness. It is not indifference: indifference is the positive claim that both directions hold, and 将无同 does not claim that either. Under Definition 1 this relation is not rational, and no utility function represents it.

Def 1a Splitting ≽ into two relations

x > y ⟺ x ≽ y but not y ≽ x strict preference

x ~ y ⟺ x ≽ y and y ≽ x indifference

Claim. If ≽ is rational then:

> is irreflexive — not x > x
> is transitive
> is anti-symmetric — x > y ⟹ not y > x
~ is reflexive, transitive and symmetric
If x > y ≽ z, then x > z

The slide's proof of the whole claim is one word: easy. The last item is the one worth doing — it is the mixed case, where a strict preference is followed by a weak one, and its proof is the only one that uses completeness.

Why The Dutch book argument

Why do we need transitivity for a rational preference? The slide's answer is a money pump.

Person P has an intransitive preference: x > y, y > z, z > x. P initially holds option x.
Merchant M sells P option z for x + ε, where ε is a small amount of money. P accepts, because z > x.
M sells P option y for z + ε. P accepts, because y > z.
M sells P option x for y + ε. P accepts, because x > y.
P is back where they started, holding x, having paid out 3ε

P has given 3ε to M for nothing. The slide adds the observation that this is possible in the market situation — the argument is not a thought experiment about an impossible agent.

The argument is a coherence argument, not a moral one. It does not say an intransitive person is foolish; it says an intransitive person's choices are not defended by any ranking, so nothing in the agent rules out the loss. Note also what it does not show: the pump requires someone to know your preference cycle and to be able to make you the offers, and each round must be worth more than ε to you.

The utility function

slide 7

Def 2 Representing a preference relation

A function u: X → R is a utility function representing the preference relation ≽ if, for all x, y ∈ X, x ≽ y ⟺ u(x) ≥ u(y).

Remark — the representation is not unique. If u represents ≽, then so does v(x) = f(u(x)) for any strictly increasing function f.

This remark is the reason “utility” in modern economics is not a quantity of anything. Only the ordering is identified; the numbers are a convenient encoding of it. It is also the licence that behavioral economics later uses to replace the utility function without abandoning maximisation.

Prop 1 Representation implies rationality

A preference relation ≽ can be represented by a utility function only if it is rational.

representation ⟹ rational preference

Proof: easy. The slide then asks the other direction and answers it in two parts.

Can any rational ≽ be described by some utility function?	No in general. Rationality alone is not enough when X is infinite — the lexicographic ordering on the plane is the standard counterexample.
If X is finite?	Yes. Claim: if X is finite and ≽ is a rational preference relation on X, then there is a utility function u: X → R representing ≽. Proof: not required

Keep the asymmetry straight, because it is an easy exam question: representation always implies rationality; rationality implies representation only under an extra condition, and finiteness of X is sufficient (not necessary).

The choice-based approach and the weak axiom

slides 8–10

The second route refuses to talk about mental attitudes at all. It starts from what people are observed to pick.

Two collectors 《世说新语 · 雅量》

祖士少好财，阮遥集好屐，并恒自经营，同是一累，而未判其得失。人有诣祖，见料视财物。客至，屏当未尽，馀两小簏箸背后，倾身障之，意未能平。或有诣阮，见自吹火蜡屐，因叹曰：“未知一生当箸几量屐？”神色闲畅。于是胜负始分。

Both Zu Shao and Ruan Yaoji had a collecting habit — one money, one clogs — and neither ranked above the other, until a visitor watched each of them handling his hoard. Zu, caught mid-count, tries to hide two baskets behind him and is visibly uncomfortable; Ruan, waxing his clogs by his own fire, sighs that he does not know how many pairs a life can wear, and is perfectly at ease. 「于是胜负始分」 — only then were they ranked.

The slide's gloss is the definition of the second approach: 从外显行为的细微之处来推测内在偏好的差异 — infer the difference in inner preference from the fine detail of outward behaviour. Choice-based analysis is based on choice rather than preference.

Def 3 The choice structure and the weak axiom

2^B is the family (set) of nonempty subsets of X. C() is a choice rule that assigns a nonempty set of chosen elements C(B) ⊆ B for every budget set B ∈ 2^B, where ∅ ∉ 2^B.

The choice structure (2^B, C()) satisfies the weak axiom (WA) of revealed preference if the following property holds:

If for some A ∈ 2^B with x, y ∈ A we have x ∈ C(A), then for any B ∈ 2^B with x, y ∈ B and y ∈ C(B), we must also have x ∈ C(B).

Remark, in the slide's own words: the weak axiom says that if x is ever chosen when y is available, then there can be no budget set containing both alternatives for which y is chosen and x is not.

Equivalently, and contrapositively: revealing a preference for x over y in one budget forbids revealing the opposite in another. The axiom is the minimum coherence you would require of a set of choices before you were willing to call them evidence about a ranking — and Proposition 3 will show it is also enough.

Model 3

The weak axiom, interactively

Set a choice function on four budgets and let the model hunt for a violation. Two of the three presets violate the axiom; the point is to see exactly which pair of budgets does it.

The Independence of Irrelevant Alternatives

slide 10

IIA Sen's Property α — a necessary condition for WA

If x ∈ B ⊆ A and x ∈ C(A), then x ∈ C(B)

In words, from the slide: x is chosen from a set of alternatives A, and B is a subset of A that contains x, then x must be chosen from B. That is, eliminating some of the unchosen alternatives shouldn't affect the selection of x as the best option.

≡ The two conditions are equivalent here, not nested

The slide presents Property α as a necessary condition for the weak axiom. For a choice rule that always returns a nonempty set — which is what Definition 3 assumes — the other direction also goes through, so on this domain the two are equivalent and either can be used as the test.

The reverse step: suppose WA holds, x ∈ C(A) and x ∈ B ⊆ A, but x ∉ C(B). Since C(B) is nonempty, pick y ∈ C(B) with y ≠ x. Now x ∈ C(A) with x, y ∈ A, and y ∈ C(B) with x, y ∈ B, so WA forces x ∈ C(B) — a contradiction.

Nonemptiness is doing real work in that argument. If C(B) were allowed to be empty the equivalence would fail — which is exactly why the deck states ∅ ∉ 2^B when it defines the choice structure.

! What IIA rules out, in one sentence

It rules out menu effects. If your choice from {x, y} depends on whether z is also on the menu, then z was not irrelevant to your choice. Every one of the six behaviors in the second half of this lecture is, formally, a menu effect — and Model 5 is the sharpest of them.

The link between the two approaches

slide 11

Prop 2 Rationality generates a choice structure that satisfies WA

Suppose that ≽ is a rational preference relation. Then the choice structure generated by ≽, written (2^B, C*(·, ≽)), satisfies the weak axiom.

Proof: easy — see MWG p. 12

Def 4 What it means to rationalise a choice rule

Given a choice structure (2^B, C()), we say that the rational preference relation ≽ rationalises C() relative to 2^B if

C(B) = C*(B, ≽) for all B ∈ 2^B

that is, if ≽ generates the choice structure (2^B, C()).

Prop 3 The converse — and this is the payoff of the whole first half

If (2^B, C()) is a choice structure such that (1) the weak axiom is satisfied, and (2) 2^B includes all subsets of X of up to three elements,

then there is a rational preference relation ≽ that rationalises C() relative to 2^B — that is, C(B) = C*(B, ≽) for all B ∈ 2^B. Furthermore, this rational preference relation is the only preference relation that does so.

Proof: not required

→ What Propositions 2 and 3 together buy you

Proposition 2 says rationality is sufficient for WA. Proposition 3 says WA plus a small richness condition on the domain is sufficient for rationality — and moreover pins the preference relation down uniquely. Together they mean that on this domain, “acts like a utility maximiser” and “satisfies the weak axiom” are the same claim.

That is why the rest of the lecture can treat the six experiments as tests of a single hypothesis. Demonstrating that a choice is menu-dependent is not a demonstration that some particular utility function is wrong; it is a demonstration that no utility function fits.

The three-element condition is not decoration. It is what gives the argument enough pairwise comparisons to build a full ordering — with only pairs available, WA can be satisfied by choice functions that no ranking generates.

Six departures from rational choice

slide 12 and the rest of the lecture

The slide lists them in one go, and the lecture then takes six slides to do them. Each entry below gets the same three things: what was done, what came out, and which axiom it breaks.

Departure	中文	The one-line version	Broken by
Mental accounting	心理账户	Money is not fungible across the accounts you keep it in	§8
Sunk cost fallacy	沉没成本谬误	Past outlays that cannot be recovered still move the current choice	§9
Framing effect	框架效应	The same options, worded differently, produce different choices	§10
Endowment effect	禀赋效应	Willingness to accept exceeds willingness to pay for the same object	§11
Status quo bias	现状偏差	People choose what they were initially given	§12
Menu dependence	菜单依赖	Adding an option nobody would pick changes what is picked	§13

Mental accounting 心理账户

slide 13

A / B The lost ticket and the lost note

(A) Imagine that you have bought a ticket for a show for $40. When you reach the theatre you discover that you have lost the ticket. You can buy another ticket at the same price. Will you do so?

(B) Imagine that you intend to go to a show. When you take your wallet out of your pocket to pay for the $40 ticket, you discover that you have lost $40, but you still have enough cash to buy a ticket. Will you do so?

Facing the same options, more people choose to buy the ticket in situation B than in situation A.
In situation A, people think of the cost of seeing the show as $40 + $40 = $80 — which feels too high.
In situation B, the lost $40 is unrelated to the ticket price. The show still costs $40.

Under mental accounting, money is nonfungible across different accounts.

Formally: the two situations have identical final-wealth consequences. Losing a $40 ticket and losing $40 are the same loss. What differs is which mental account the loss is booked against — the entertainment account in A, some general account in B.

! Identify the violation precisely

Note which axiom this breaks, because it is not the obvious one. Preferences over final wealth are perfectly consistent here; nothing about transitivity is at stake. What fails is the definition of the budget set itself: if money is not fungible, then the feasible set is not the set of affordable bundles, and the objects being chosen are not the ones the theory is ranking. The subject in A is choosing between “show at an effective price of $80” and “no show”; the subject in B is choosing between “show at $40” and “no show”.

Sunk cost 沉没成本

slides 14–16

In scenario (A) above, people's buying decision is influenced by the lost ticket. The lecture's statement of the standard: a sunk cost should not be considered in rational decision making — don't cry over spilled milk.

王子猷 and the trip he did not finish 《世说新语 · 任诞》

王子猷居山阴，夜大雪，眠觉，开室，命酌酒。四望皎然，因起仿偟，咏左思招隐诗。忽忆戴安道，时戴在剡，即便夜乘小船就之。经宿方至，造门不前而返。人问其故，王曰：“吾本乘兴而行，兴尽而返，何必见戴？”

Wang Ziyou wakes to snow, drinks, recites a poem, suddenly remembers his friend Dai Andao, and sets off by boat at night. He travels all night, arrives at the door, and turns around without knocking. Asked why: “吾本乘兴而行，兴尽而返，何必见戴？” — I set out on an impulse and I turn back when the impulse is spent; why must I see Dai?

The slide reads this as the sunk cost fallacy inverted and avoided: a night's travel is a large unrecoverable outlay, and the reason for the trip — the impulse — is what justifies the trip, not the distance already covered. When the impulse is exhausted, so is the reason. The cost already paid is correctly ignored. (The slide's own gloss: 「沉没之费，或舍或执」 — the sunk cost is either released or clung to.)

Field Do Singapore's expensive cars get driven more?

Ho, Png and Reza (2016). Buying a car in Singapore carries a very high sunk cost — the Certificate of Entitlement, taxes, and so on.

High-sunk-cost cars drive more.
Driving time decreases with the car's age.
The decrease between driving time and car age is larger for the high-sunk-cost cars.

The third finding is the one that identifies the mechanism. All cars are driven less as they age; what matters is that the expensive ones decay faster toward the common level — the signature of a sunk-cost effect wearing off as the outlay recedes into the past.

The figure on the slide plots average monthly usage by car age for three registration years, with average sunk costs of 16,921, 15,301 and 13,261 Singapore dollars, for the most popular model in the sample (3,403 cars). Usage starts high — around 2,700 km a month at five months — and flattens near 1,500 km by the mid-80s. The ordering of the three lines follows the ordering of the sunk costs for most of the range, which is the regression's raw material. The vertical axis is in kilometres and the sunk costs are in Singapore dollars — the figure's own note reads “average sunk cost S$”, which is the standard abbreviation for the Singapore dollar.

Framing effect 框架效应

slides 17–21

朝三暮四《庄子 · 齐物论》

狙公赋芧，曰：“朝三而暮四。”众狙皆怒。曰：“然则朝四而暮三。”众狙皆悦。名实未亏而喜怒为用，亦因是也。

The monkey keeper announces three chestnuts in the morning and four in the evening, and the monkeys are furious; he offers four in the morning and three in the evening, and they are delighted. 「名实未亏而喜怒为用」 — the substance is untouched, yet joy and anger were put to work. 「狙：猴子」

Zhuangzi's own verdict is the framing effect stated sixteen centuries early: the total is the same and the reaction is not. The slide's question, 你能解释这一结果吗？, is answered by the Asian disease experiment a slide later.

1981 Tversky & Kahneman, the Asian disease problem

Two versions of the same problem, given to two different groups. N = 152 saw the first, N = 155 saw the second.

Framed as lives saved	Chose
Program A — 200 people will be saved	72%
Program B — 1/3 probability that 600 will be saved, 2/3 probability that no one will be saved	28%

Framed as lives lost	Chose
Program C — 400 people will die	22%
Program D — 1/3 probability that nobody will die, 2/3 probability that all 600 will die	78%

A and C describe exactly the same outcome: 200 saved out of 600 is 400 dead out of 600.
B and D describe exactly the same lottery.
Yet A beats B by 72% to 28% when framed as saved, and C loses to D by 22% to 78% when framed as lost.
The reversal is complete: the modal choice in the first frame is the least popular option in the second.

Under the “saved” frame people are risk-averse — take the certain 200. Under the “died” frame they are risk-seeking — take the gamble. Same outcomes, opposite attitude to risk.

Why Why this is a violation of rationality

The preference is not stable: x > y in one frame, while y > x in another frame. A preference relation is a function of the alternatives; if it changes with the description, it is not a function of the alternatives.

Slide 21's statement of the general phenomenon is worth keeping verbatim: framing effects: people change their choices when the changes in the options are inconsequential — different wordings, settings, and situations.

Connect this back to §2. The reversal is a violation of completeness as a property of a fixed relation, not of transitivity. And connect it forward: the mechanism is the same reference-point shift as in the two-question experiment of Lecture 1 — “lives saved” makes 600 alive the reference point, “lives lost” makes 600 dead the reference point.

Endowment effect 禀赋效应

slides 22–23

1990 Kahneman, Knetsch & Thaler, the mug experiment

44 subjects. Half are randomly given mugs, the other half are given nothing. Owners state the price at which they would sell; non-owners state the price at which they would buy. The price is elicited by the Becker–DeGroot–Marschak (BDM) procedure, and the market price is determined by the supply and demand curves.

Neoclassical prediction. Assignment was random, so the two groups' valuations should have the same distribution — and half the mugs, 11, should trade.
Observed. The number of mugs traded was 4, 1, 2 and 2 across the four sessions.
Median seller's value: $5.25
Median buyer's value: $2.75

Willingness to Pay (WTP) < Willingness to Accept (WTA). The gap is roughly a factor of 1.9.

Why it is a violation of rationality? The value of the object changes with ownership. People want to give additional valuation to an object when they own it. The lecture names the mechanism: loss aversion.

→ Why random assignment is what makes the experiment work

If the owners had been the people who liked mugs most, WTA > WTP would be no finding at all — it would just be selection. Randomising who gets a mug equalises the two groups' tastes in expectation, so the only thing that differs between them is ownership. Everything hangs on that.

And why BDM rather than asking for a price: BDM makes truthful revelation weakly dominant. You state your value; if the randomly drawn market price beats it you trade, otherwise you do not. Since misreporting can only make you worse off, the stated number is the real one.

Model 4

The mug market

Twenty-two owners and twenty-two non-owners. At λ = 1 the market clears at exactly the 11 mugs neoclassical theory predicts; raise λ and see where it goes.

Status quo bias and defaults 现状偏差

slides 24–28

Status quo bias: people choose an object which they are initially given. The lecture's statement of why that violates rationality is precise — the choice of {donate, not donate} depends on the initial condition.

2003 Johnson & Goldstein — how to get more organ donations

The question posed: a large educational campaign? The slides' answer is that most public policy choices have a no-action default — a condition imposed when an individual fails to make a decision — and the default does more work than the campaign.

Regime	What it means
Presumed consent opt-out	People are organ donors unless they register not to be
Explicit consent opt-in	Nobody is an organ donor without registering to be one

Study 1 — online experiment. 161 subjects were asked whether they would be donors under three conditions:

Opt-in condition — subjects assume they have just moved to a state where the default is not to be a donor, and are given the choice to confirm or change that status by clicking.
Opt-out condition — the default is to be a donor.
Neutral condition — no prior default.

Study 2 — cross-country difference in Europe. The same variable measured in the field.

! A result the deck does not give

Study 1's design is on the slide in full — the three conditions, the subject count, the mechanism — but its results are not. The numbers are not on the slide and are not quoted here. Study 2's results are on the slide, as the bar chart below, and those are the figures the lab uses.

王敦 at the lavatory 《世说新语 · 纰漏》

王敦初尚主，如厕，见漆箱盛乾枣，本以塞鼻，王谓厕上亦下果，食遂至尽。既还，婢擎金澡盘盛水，琉璃碗盛澡豆，因倒箸水中而饮之，谓是乾饭。群婢莫不掩口而笑之。

Wang Dun, newly married into the imperial family, visits the privy and finds dried dates in a lacquered box — put there to hold under the nose against the smell — and eats them all, taking them for refreshments. Returning, he is offered water in a golden basin and bath-beans in a glass bowl, and tips the beans into the water and drinks it, taking it for a rice dish. The maids cover their mouths.

The slide's gloss: 人们到了一个新的环境，往往还是采用旧的选择习惯，产生差错 — arriving in a new environment, people still apply their old choice habits, and get it wrong. This is the status quo bias viewed from the inside: the default he carried with him was his own past.

Why Three explanations, and the policy consequence

Inertia / omission effect

Doing nothing is not experienced as a choice, so it carries no responsibility.

Suggestion

The default is read as advice — as what the designer thinks you should do.

Loss aversion

Moving off the default means giving something up, and losses weigh more than gains.

The consequence

The lecture's own conclusion: default is one of the most powerful methods to do behavioral nudge.

All three explanations can be true at once, and they carry different welfare implications — a point worth holding on to when you evaluate a default as policy. A default that corrects inertia helps the inattentive; the same default imposes a choice on someone who simply had not got round to registering.

Model 6

Defaults and the status quo

The eleven-country consent chart from the slide, plus a two-parameter model of what a default actually does. Nearly the whole international spread comes out of the model.

Menu dependence

slides 29–32

Asymmetric dominance — the decoy effect

1982 Huber, Payne & Puto — beer

Subjects choose between two types of beer.

Option 1 — $1.80 per six pack, quality rating 50.
Option 2 — $2.60 per six pack, quality rating 70.
Result: 43% chose Option 1, 57% chose Option 2.
A third option is added, strictly dominated by Option 1: $1.80 per six pack, quality rating 40.
Result: 63% now choose Option 1.

Option 3 cannot be chosen by anyone maximising on price and quality — it is worse than Option 1 on both. Yet its presence moves Option 1 from 43% to 63%.

≡ Why this is a violation of IIA, step by step

Set A = {x1, x2, x3} and B = {x1, x2}, with x1 the target.

Property α says: if x1 ∈ B ⊆ A and x1 ∈ C(A), then x1 ∈ C(B). In proportions: the share choosing x1 should be the same in the two situations.

In the experiment the share choosing x1 facing the large set A is higher than the share facing the small set B — 63% against 43%. That is the contradiction. The slide's closing question, and the one to carry away: how to explain this asymmetric dominance effect? Reason-based choice?

The compromise effect

1989 Simonson — calculator batteries

Subjects choose between two types of calculator batteries.

Scenario 1. Option 1 — lifespan 12 hours, 2% probability of corrosion. Option 2 — lifespan 14 hours, 4% probability of corrosion.
Result: 43% chose Option 2.
Scenario 2. A third option is described: Option 3 — 16 hours, 6% probability of corrosion.
Result: 60% chose Option 2.

Option 2's share rises from 43% to 60% purely because a third option was described. The slide's own note: the analysis is similar to the asymmetric dominance effect (please verify it).

What changes is Option 2's position, not its attributes. In Scenario 1 it is an extreme — the longest life and the highest corrosion risk. In Scenario 2 it is the interior point of a three-point range. Model 5 plots both experiments on the same two axes so the difference between the two mechanisms is visible.

Model 5

Decoy and compromise

Two experiments, two mechanisms, one violation. Switch the third option on and off and watch the shares move.

A slip of the tongue 《世说新语 · 排调》

孙子荆年少时欲隐，语王武子“当枕石漱流”，误曰“漱石枕流”。王曰：“流可枕，石可漱乎？”孙曰：“所以枕流，欲洗其耳；所以漱石，欲砺其齿。”

Young Sun Zijing means to say he will “pillow on stones and rinse in the stream”, and misspeaks: he says “rinse on stones and pillow on the stream”. Wang challenges him, and Sun improvises a defence — pillowing on the stream to wash out his ears, rinsing on stones to sharpen his teeth. 请问在这则故事中，王武之的口误是否是理性行为？这类错误是否是系统性偏误？

The answer the framework gives: the slip itself is noise — a single token transposition with no direction, and therefore not a behavioral finding under the three properties of Lecture 1. The rationalisation is the interesting part: the recovery is itself systematic, because people reconstruct a reason for what they have already done far more reliably than they predict what they will do. The slide's closing couplet makes the same point — 「枕流漱石，口误可以辞饰；系统之偏，终非辞之所掩」: a slip can be dressed up in words; a systematic bias cannot be hidden by them.

Summary sheet

printable

Rational preference · Definition 1

≽ on X is rational if complete (for all x,y: x ≽ y or y ≽ x) and transitive (if x ≽ y and y ≽ z then x ≽ z).

Derived relations · Definition 1a

x > y ⟺ x ≽ y but not y ≽ x · x ~ y ⟺ x ≽ y and y ≽ x. The slide's claim: > is irreflexive, transitive and antisymmetric; ~ is reflexive, transitive and symmetric.

Utility function · Definition 2

u: X → R represents ≽ if for all x, y: x ≽ y ⟺ u(x) ≥ u(y). Not unique — v = f(u) for any strictly increasing f represents the same ≽.

Both directions, stated exactly

Proposition 1: representation ⟹ rational. The converse needs an extra condition: if X is finite and ≽ is rational, a representing u exists.

Choice structure · Definition 3

2^B is the family of nonempty subsets of X; C() assigns a nonempty C(B) ⊆ B to every B ∈ 2^B.

The weak axiom

If for some A with x, y ∈ A we have x ∈ C(A), then for any B with x, y ∈ B and y ∈ C(B), we must also have x ∈ C(B).

Sen's Property α / IIA

x ∈ B ⊆ A and x ∈ C(A) ⟹ x ∈ C(B)

Stated on the slide as a necessary condition for WA; equivalent to it when C() is nonempty-valued.

Rationalisation · Definition 4

C(B) = C*(B, ≽) for all B ∈ 2^B

≽ rationalises C() relative to 2^B.

The two propositions that close the first half

Proposition 2: rational ≽ ⟹ the generated choice structure satisfies WA.
Proposition 3: WA + every subset of up to three elements ⟹ a rational ≽ rationalises C(), and it is the only one that does.

Headline numbers

Asian disease: 72 / 28 under the saved frame, 22 / 78 under the died frame. Mug market: 11 predicted trades against 4, 1, 2, 2 observed; median WTA $5.25 against median WTP $2.75. Beer decoy: 43% → 63%. Batteries: 43% → 60%.

Key concepts

English term · 中文

Term	中文	Meaning in this lecture
Preference relation	偏好关系	A binary relation ≽ on X; the model's primitive on the preference-based route.
Completeness	完备性	Every pair is comparable — x ≽ y or y ≽ x or both.
Transitivity	传递性	x ≽ y and y ≽ z implies x ≽ z. The Dutch book is the argument for it.
Utility function	效用函数	A numerical representation of ≽, unique only up to a strictly increasing transformation.
Choice structure	选择结构	The pair (2^B, C()) — budgets and the rule that picks from them.
Weak axiom (WA)	弱公理	Being chosen over y once forbids losing to y anywhere else.
IIA / Sen's Property α	无关备择项独立性	Eliminating unchosen alternatives must not change the choice. Equivalently, no menu effects.
Rationalisation	理性化	A preference relation that generates exactly the observed choice function on every budget.
Mental accounting	心理账户	Money is nonfungible across the accounts it is mentally booked to.
Sunk cost fallacy	沉没成本谬误	Allowing an unrecoverable past outlay to influence the current decision.
Framing effect	框架效应	The choice changes when the options are inconsequentially reworded. Asian disease problem.
Endowment effect	禀赋效应	WTA > WTP for an object randomly assigned. Mechanism: loss aversion.
Status quo bias	现状偏差	Choosing what you were initially given. The basis of the default as a policy tool.
Default	默认选项	The condition imposed when an individual fails to make a decision.
Asymmetric dominance / decoy	不对称占优 · 诱饵效应	A dominated third option raises the share of the option that dominates it.
Compromise effect	折中效应	Adding an extreme option raises the share of whatever becomes the interior point.
BDM procedure	BDM 机制	Becker–DeGroot–Marschak elicitation; makes truthful valuation reporting a dominant strategy.

Self-check

graded, with explanations

0 / 0 correct

The two approaches

Q1The slide asks: if 阮宣子's “将无同” is taken as a preference relation, what is it? Which axiom does it fail?

Correct.Indifference is the positive claim that x ≽ y and y ≽ x. “将无同” asserts neither direction with confidence, so it fails completeness — the requirement that a ranking exist. Option D is true as a statement about relations in general and irrelevant here: Definition 1 is a definition of rational preference, not of relation.

Not quite.Distinguish “does not rank” from “ranks as equal”. Indifference requires both directions of ≽ to hold; a hedge asserts neither. And a relation that fails to rank some pair is still a relation — it just is not a rational one under Definition 1.

Q2Proposition 1 says a representable preference relation must be rational. What about the converse?

Correct.The slide answers the converse in two steps: “No in general”, then a claim — if X is finite and ≽ is rational on X, then a representing u: X → R exists. Keep the asymmetry: representation ⟹ rational, always; rational ⟹ representation, only with an extra condition.

Not quite.Go back to the slide with the converse question on it. The answer is neither “always” nor “never”: it is “no in general”, followed by a claim that adds a condition on X.

Q3State the weak axiom in your own terms. Which of these is it?

Correct.That is the slide's own remark almost verbatim. Option C is a stronger and different condition — it forbids any menu effect at all, whereas WA only constrains the case where the newly added option is chosen. Option B is not required: C(B) is a set, and ties are allowed.

Not quite.C is tempting but too strong: WA constrains what happens when a new option is added and chosen. Adding an option that nobody picks, in a choice function that satisfies WA, is still allowed to change nothing. And B is not part of the definition — C(B) may contain several elements.

Q4Proposition 3 requires that 2^B include all subsets of X of up to three elements. Why is that condition there?

Correct.WA constrains pairs; to recover a relation that ranks every pair you need the pairs to sit inside larger budgets that link them together. Without a richness condition on the domain, WA can be satisfied by choice functions that no ranking generates — which is why the condition is in the statement rather than buried in the proof.

Not quite.It is a domain condition, not a proof convenience. WA on its own is a statement about pairs of alternatives; Proposition 3 needs to weld those pairwise judgements into one ordering over all of X, and for that the domain has to be rich enough.

The departures

Q5In the lost-ticket problem, more people buy a replacement ticket in situation B (lost $40 cash) than in situation A (lost the $40 ticket). What exactly is irrational about that?

Correct.Losing a $40 ticket and losing $40 leave you in the same position. The slide's own explanation is that in A the ticket is felt to cost $80, while in B the lost $40 is “unrelated to the ticket price” — which is the definition of money being nonfungible across accounts.

Not quite.Check the final wealth: you began with enough cash for a ticket plus a ticket's worth of value, and you end without the ticket either way. Nothing about transitivity or time is at stake; what is at stake is which account the loss is charged to.

Q6The Asian disease problem gives 72%/28% under the “saved” frame and 22%/78% under the “died” frame. Why does the lecture call this a violation of rationality rather than a change in circumstances?

Correct.Program A and Program C are the same outcome — 200 of 600 saved is 400 of 600 dead — and B and D are the same lottery. The probabilities are identical; only the description moved. A preference relation is a function of the alternatives, and this one moves when only the description moves.

Not quite.The probabilities and the outcomes are identical across the two frames — that is what makes it a framing effect. Check the mapping: A vs C are the same outcome, B vs D are the same lottery. And note D is simply false: the modal choice flips from risk-averse to risk-seeking.

Q7Kahneman, Knetsch and Thaler randomly gave mugs to half of 44 subjects. Why is the random assignment essential to the result?

Correct.Without randomisation, WTA > WTP would just mean mug-lovers got the mugs. Randomisation removes the selection story, leaving ownership as the only difference. B is a consequence of random assignment plus common valuations, not the reason for it; C is a property of BDM, which works whatever the assignment.

Not quite.Ask what alternative explanation the design is closing off. If owners had self-selected into owning, a WTA–WTP gap would be no finding at all. Randomisation is what makes the comparison informative — and it is what makes the 11-mug prediction meaningful too.

Q8In the beer experiment, the third option ($1.80, rating 40) is strictly dominated by Option 1 ($1.80, rating 50). Yet adding it raised Option 1's share from 43% to 63%. Which axiom does that violate?

Correct.With A = {x1, x2, x3} and B = {x1, x2}, Property α requires the share choosing x1 to be the same in both. Here it is 63% from A against 43% from B. Note the direction — the violation is that the share is higher in the larger set, which is what the attraction effect produces and what a utility maximiser cannot.

Not quite.Option C is the trap. Adding a strictly worse option cannot change a utility maximiser's choice at all, so if anything the share should be unchanged, not raised. The relevant axiom is the one that says eliminating unchosen alternatives must not affect the selection — and here the share moves the wrong way.

Q9Show that Sen's Property α and the weak axiom are equivalent, given that C(B) is nonempty for every budget. State exactly where nonemptiness is used.

Set-up. Write the two conditions as
WA: for all A, B and all x, y ∈ A ∩ B, if x ∈ C(A) and y ∈ C(B) then x ∈ C(B).
α: for all A, B with B ⊆ A and all x ∈ B, if x ∈ C(A) then x ∈ C(B).

α ⟹ WA. Let x ∈ C(A) and y ∈ C(B) with x, y ∈ A ∩ B. Since x ∈ C(A) and x ∈ B ⊆ A, Property α gives x ∈ C(B) directly. No extra assumption is used.

WA ⟹ α. Let x ∈ C(A) with x ∈ B ⊆ A, and suppose for contradiction that x ∉ C(B). Nonemptiness is used here: since C(B) is nonempty we may pick y ∈ C(B), and since x ∉ C(B) this y differs from x. Now x ∈ C(A) with x, y ∈ A, and y ∈ C(B) with x, y ∈ B, so WA forces x ∈ C(B) — contradicting x ∉ C(B). Hence x ∈ C(B).

Where nonemptiness is load-bearing. If C(B) were allowed to be empty the step “pick y ∈ C(B)” would fail, and the implication would break: a choice rule that returns an empty set from some budget can satisfy WA vacuously — there is no y ∈ C(B) to trigger it — while violating α outright. That is why Definition 3 builds C(B) nonempty, and why the deck writes ∅ ∉ 2^B when it defines 2^B.

Why the slide calls α a “necessary condition”. α ⟹ WA is the direction that justifies the label. The slide does not need the converse, but it holds on this domain — which is useful, because it means either condition can be used as the test. Model 3 tests α directly.

Lecture 3

Belief

Source: lecture 3 belief revision EN.pptx — 44 slides Kahneman (2003), Tversky & Kahneman (1974) Five 《世说新语》 cases

Lectures 1 and 2 asked what a choice is. This lecture asks what a belief is — how a probability gets formed when nobody hands you one, and why the answer departs from the statistician's answer in predictable directions. The deck opens with two questions it returns to throughout: a positive COVID-19 test means what, exactly, and who forecasts tomorrow's stock market better — you, an expert, or the market price?

The organising distinction is stated on slide 3 and never dropped: normative theory says how beliefs should be formed; behavioral theory describes how they are formed, and uses the gap between the two to identify the underlying judgment process. Every phenomenon below is therefore paired with the norm it violates — independence, the law of large numbers, the conjunction rule, Bayes' rule, or calibration. Without the benchmark, “bias” is just a word.

The deck is mostly text, but seven slides are image-only or image-led. The class's own Bayesian-updating chart (slide 15) and the two-system diagram (slide 6) were read off the rendered slide. The chart on slide 15 carries no explanatory caption beyond the treatment parameters, so the workbench describes what it plots and does not invent the experiment's instructions.

Concept map

from the two systems to a price

How is a belief formed?Not by calculating the statistic. By substituting an easier question whose answer comes to mind.

the machinery

System 1Fast, parallel, automatic, associative, emotional.

System 2Slow, serial, controlled, effortful, rule-governed — and not always engaged.

Attribute substitutionJudge a hard target attribute by an accessible proxy, without noticing the swap.

the three heuristics, and the norms they break

RepresentativenessSimilarity to a process stands in for its probability.

AvailabilityEase of recall stands in for frequency.

AnchoringA starting value stands in for the estimate.

Norms violatedIndependence · law of large numbers · conjunction rule · Bayes' rule · calibration

beliefs about one's own beliefs

OverconfidenceOverestimation, overplacement, overprecision.

ElicitationA belief is only as good as the rule that pays for it.

Prediction marketsCan individual errors cancel in the aggregate?

when belief leaves reality behind

Correlation ≠ causationOne co-occurrence is not a forecast.

Motivated beliefsBeliefs yield utility directly, so they bend toward what is welcome.

Real consequencesA false belief can still change behavior and physiology.

The two-system view

slides 5–10

Kahneman (2003, American Economic Review) distinguishes three cognitive systems, but the economically relevant division is between the first two. Perception and intuition (System 1) are fast and automatic; reasoning (System 2) is slow, controlled and rule-governed. The implication is not that one is better. It is that System 1 always produces an answer, and System 2 has to check it — and checking is costly.

Process	Perception / intuition · System 1	Reasoning · System 2
Speed	Fast	Slow
Architecture	Parallel	Serial
Control	Automatic	Controlled
Effort	Effortless	Effortful
Mode	Associative, emotional	Rule-governed, flexible, neutral
Content	Percepts, current stimulation, stimulus-bound	Conceptual representations, past and future, evokable by language

Reconstructed from Figure 1 of Kahneman (2003), which the slide reproduces. The slide labels the middle box “INTUITION · SYSTEM 1” and the right box “REASONING · SYSTEM 2”.

CRT The bat and the ball

A bat and a ball cost $11 in total. The bat costs $10 more than the ball. How much does the bat cost? Answer within three seconds, without calculating. (Frederick, 2005, JEP.)

System 1's answer: bat $10, ball $1. This satisfies only x + y = 11; it fails 10 − 1 = 9 ≠ 10.
The intuition has quietly replaced “$10 more” with “$10”.
System 2's check: solve x + y = 11, x − y = 10 → x = 10.50, y = 0.50.

Norm violated: all constraints must hold jointly. Intuition checked one of them and stopped.

Stroop When the two systems disagree

Name the ink colour, ignoring the word. Naming is faster when word and colour agree, and slower when they conflict. In red ink, naming the colour of “green” takes longer than naming the colour of “mouse”.

A two-system reading. Reading is automatic: the word's meaning intrudes uninvited (System 1). Naming the ink colour requires suppressing that meaning (System 2). When the two conflict, response times and errors rise.

Stroop (1935). The slide's stimulus set: 红色 red · 绿色 green · 蓝色 blue · 橘色 orange · 老鼠 mouse · 企鹅 penguin · 猴子 monkey.

Which is farther, Chang'an or the sun? 《世说新语 · 夙惠》

晋明帝数岁，坐元帝膝上。有人从长安来，元帝问洛下消息，潸然流涕。明帝问何以致泣？具以东渡意告之。因问明帝：“汝意谓长安何如日远？”答曰：“日远。不闻人从日边来，居然可知。”元帝异之。明日集群臣宴会，告以此意，更重问之。乃答曰：“日近。”元帝失色，曰：“尔何故异昨日之言邪？”答曰：“举目见日，不见长安。”

The child emperor first says the sun is farther: no one has ever come from the sun. The next day, asked again before the ministers, he says the sun is nearer: he can see the sun, but not Chang'an. Both answers are wrong, and both are produced by a fast, confident cue.

The slide's reading is the one the whole lecture uses. Day one: distance is inferred from how often travellers arrive — an availability cue. Day two: distance is inferred from how readily the object is perceived — also availability. Both cues usually work. Neither measures distance itself. The question the lecture asks is exactly the child's situation: what simple rules do people use when they cannot calculate, and when do those rules err systematically?

Attribute substitution

slides 11–14

Def The mechanism underneath the heuristics

“… when an individual assesses a specified target attribute of a judgment object by substituting another property of that object — the heuristic attribute — which comes more readily to mind.” — Kahneman (2003, p. 1460)

1 · Target inaccessible

The attribute that should be judged is hard to assess directly.

2 · Proxy accessible

A related attribute comes to mind quickly.

3 · Swap unnoticed

The reflective system fails to detect and correct it.

The politician's rule: answer the question you wish you had been asked, not the one you were asked.

Setting	Target attribute	Substituted attribute
Risk as feelings (Loewenstein et al., 2001)	“How likely is it to kill you?”	“Does it scare you?”
Job interview	“Will this person do the job well?”	“Do I like this person? Do they seem sincere?”
Availability	“How frequent is this event?”	“How easily does an instance come to mind?”
Anchoring	“What is the value?”	“What value was I shown?”

Two consequences follow directly from the slide. First, dread and perceived control move risk judgments: terrorism, a catastrophe that feels uncontrollable, is overestimated. After 9/11 some Americans drove instead of flying, and road deaths rose (Gigerenzer, 2004). Second, unstructured interviews predict job performance poorly, partly because liking stands in for an assessment of ability.

↗ The lecture's own online experiment

Slide 14 sends students to veconlab.com: log in as Participant, enter session yfnj28, choose a name and password, and follow the instructions. Sessions are time-limited; the link is recorded here because the data from that run are what slide 15 plots.

(1) Representativeness

slides 16–19

Representativeness — judging the probability that an outcome came from a process by how similar the outcome is to that process.

Law of small numbers

Exaggerating how closely small samples resemble the population they are drawn from. A short run is expected to look like the long run.

Gambler's fallacy

Believing that deviations from average behaviour will be corrected in the short run: after three heads, tails “is due”.

! Norm violated

The law of large numbers holds only in large samples; independent events do not self-correct. A short sequence has no obligation to look like its generator.

Classroom Coin sequences

A fair coin is tossed six times. Which sequence is more likely?
(1) H T H T T H (2) H H H T T T
If the first three tosses are all heads, what is the probability that the fourth is heads?

Both sequences have probability (1/2)⁶ = 1/64. Order does not change the count.
Sequence (1) looks more random, so it is judged more likely — representativeness at work.
The fourth toss is still heads with probability 1/2. Expecting tails is the gambler's fallacy.

Norm violated: independence — tosses do not affect one another.

Linda The conjunction fallacy

Linda is 31, single, outspoken and very bright. She majored in philosophy. As a student she was deeply concerned with discrimination and social justice, and joined anti-nuclear demonstrations. Which is more probable?
A. Linda is a bank teller.
B. Linda is a bank teller and active in the feminist movement. Tversky & Kahneman (1983).

Most respondents choose B, implying P(feminist bank teller) > P(bank teller).
The description fits the feminist stereotype, and similarity overrides probability.
Result: the conjunction is overestimated.

Norm violated: the conjunction rule, P(A ∧ B) ≤ P(A). A subset cannot be more likely than its superset.

Bayes' rule and base-rate neglect

slides 20–21

Posterior = likelihood × prior ÷ total probability of the evidence. The denominator is the law of total probability. This is the core benchmark for every probability bias in the lecture — the slide says so in its “Norm violated” strip.

Model 7

What a positive test actually means

The opening question of the lecture, made movable. Set prevalence, sensitivity and the false-positive rate; the grid shows 1,000 people, and the posterior is the share of positives who are genuinely ill. The default is Eddy's (1982) breast-cancer screening example.

Eddy 1982 Breast-cancer screening

Prevalence Pr(C) = 1%. Sensitivity Pr(P | C) = 90%. False-positive rate Pr(P | ¬C) = 10%.

Posterior: Pr(C | P) = (0.9 × 0.01) / (0.9 × 0.01 + 0.1 × 0.99) = 0.009 / 0.108 ≈ 8.3%.
Most people — including some physicians — estimate far higher.
The base rate is doing most of the work: the disease is rare, so most positives are false.

Natural frequencies (Gigerenzer & Hoffrage, 1995): of 1,000 women, 10 have cancer and 9 of them test positive; of the 990 healthy, about 99 test positive. So 9 of 108 positives — about 8% — have cancer. The same arithmetic, in a format that does not require handling a conditional probability.

The slide's questionnaire note: prevalence varies by age, and so does the meaning of a positive test. A single 8% is therefore an illustration, not a constant.

? Why the norm matters here

Base-rate neglect is not a failure to multiply. It is a failure to condition: the representativeness of the symptom (a positive test) replaces the prior probability of the disease. The natural-frequency format works because it turns the conditional into a count, and counts are what System 1 handles well.

▤ The class's own updating data (slide 15)

The slide carries a result from the instructor's run: 53 participants, dated 24 September 2026, treatment with prior Pr(Red cup) = 0.50 and likelihoods Pr(R | R cup) = Pr(B | B cup) = 0.67, payoffs $2.00 or $0.00. The chart plots each participant's reported probability against the stated probability of the red cup, with the median and mean shown and the Bayesian prediction as the reference line.

The medians sit close to the 45° reference at every stated probability; the mean is noisier at the ends. What the slide does not give is the instruction that produced the reports, so the workbench stops at describing the plot. What it can say is that this classroom run is much better calibrated than the survey evidence below — which is what the next slide's lab experiments also find.

Experimental evidence on belief updating

slide 22

Study	Design	Departure from Bayes
Bingo cages Grether (1980, QJE)	Two cages hold balls in different proportions; the prior is announced. Subjects see draws with replacement and judge which cage was used.	When a sample resembles one cage, subjects overweight the sample and underweight the prior — though less than in survey studies.
Self-relevant news Möbius et al. (2022, MS)	After an IQ test, subjects receive noisy signals about their rank.	Updates move in the Bayesian direction but too little (conservatism). Good news moves beliefs more than bad news (asymmetric updating).

The two studies point in opposite directions on the surface — over-reaction to a sample in one, under-reaction to a signal in the other — and the lecture uses the contrast to make a larger point. Belief biases stem not only from computational limits but also from a preference over self-image. The bingo-cage subject has no stake in which cage it was; the IQ-test subject does.

! Norm violated

Bayes' rule: prior and likelihood should be combined with the weights the rule prescribes. Both overweighting the likelihood and underweighting it are failures of the same benchmark.

(2) Availability

slide 23

Letter r The classic demonstration

In English words, is the letter r more often the first letter or the third? Tversky & Kahneman (1973).

Most people say first, because words beginning with r are easier to recall — you can generate them by running the alphabet.
In fact, r appears more often in third position. Retrieval by first letter is easier, and ease is mistaken for frequency.

General mechanism: frequency or probability is judged by how easily instances come to mind. Heavily reported, vivid events such as plane crashes are overestimated.

This is the mechanism behind the opening 长安 / 日 exchange: “has anyone come from there” and “can it be seen” are both availability cues, and both are silent about distance. It is also the mechanism behind risk as feelings: a vivid, dread-laden hazard is overestimated relative to a statistical one.

! Norm violated

Frequency judgments should rest on the population distribution, not on ease of recall. The two coincide only when memory is a faithful sample of the population — which is exactly what media coverage and vividness break.

(3) Anchoring, and compound events

slides 24–26

Wheel African nations in the UN

After spinning a visibly random wheel, subjects estimate the percentage of UN members that are African. Tversky & Kahneman (1974).

Anchor 10 → median estimate 25.
Anchor 65 → median estimate 45.
An irrelevant starting value still moves the estimate. System 2 must work to escape it, and adjustment is typically insufficient.

Classroom experiment: write down the last two digits of your student ID. Would you buy an NJU cap for that many yuan? What is the most you would pay? Prediction: students with higher digits state higher WTP. See “coherent arbitrariness” in Ariely, Loewenstein & Prelec (2003, QJE).

The slide gives the two medians and the anchors, but not the true African share in the UN — so the workbench does not supply one. The point is the difference between the two groups, not either estimate's accuracy.

! Norm violated

Estimates should depend only on relevant information; a starting value should not change them. The wheel is visibly random, so there is no information in it to justify any movement at all.

6/49 Judging compound events

Pick 6 of 49 numbers, order irrelevant; all six correct wins the jackpot. What is the probability?

6/49 × 5/48 × 4/47 × 3/46 × 2/45 × 1/44 = 1 / 13,983,816

Conjunctive events · overestimated

Winning requires six events together: about 1 in 13,983,816. People anchor on the single-draw chance 6/49 and adjust down too little. The slide's analogy: draw six aces in a row from 49 cards containing six aces.

Disjunctive events · underestimated

In a class of 30 (same non-leap year, uniform birthdays), the chance that at least two share a birthday is about 70.6%. No shared birthday: 365/365 × 364/365 × … × 336/365 ≈ 29.4%. People anchor on the single-pair chance, 1/365, and adjust up too little.

Norm violated: compound probabilities must be computed from all components, not anchored on one.

Overconfidence

slides 28–31

Overestimation

Believing your absolute performance is better than it is. E.g. students predicting exam scores.

Overplacement

Believing your relative rank is higher than it is: “all the children are above average”. See the questionnaire.

Overprecision

Excessive certainty about your judgments; confidence intervals too narrow. E.g. the length of the Amazon.

Classification: Moore & Healy (2008, Psychological Review). A related bias is optimism: believing good things are more likely to happen to you.

Competitor neglect Why every studio opens on the same weekend

“Is my film good?” replaces “Is my film better?” — Disney studio head Joe Roth, on why big films crowd into the holidays. Camerer & Lovallo (1999, AER), quoting the Los Angeles Times (1996).

Overplacement does not require believing you are good in absolute terms. It requires only forgetting that everyone else is asking the same question about their own film.

Intervals Overprecision

Share of true values falling outside stated 90% confidence intervals: ≈ 50%. Alpert & Raiffa (1982); Klayman et al. (1999).

A policy example: on 7 February 2003, U.S. Defense Secretary Donald Rumsfeld told troops in Aviano, Italy, that a conflict with Iraq could last six days or six weeks, and that he doubted it would last six months. The conflict and deployment lasted years.
Experts are not exempt: physicians and financial analysts also show overconfidence in forecasts, knowledge recall, self-assessment and judgments of control.

Norm violated: calibration — 90% intervals should contain about 90% of true values. At 50% outside, the intervals are behaving like 50% intervals.

Jing Fang and hindsight 《世说新语 · 规箴》

京房与汉元帝共论，因问帝：“幽、厉之君何以亡？所任何人？”答曰：“其任人不忠。”房曰：“知不忠而任之，何邪？”曰：“亡国之君，各贤其臣，岂知不忠而任之？”房稽首曰：“将恐今之视古，亦犹后之视今也。”

Jing Fang asks why the kings You and Li fell. The emperor answers: they employed disloyal men. “Why employ them, knowing they were disloyal?” “Every ruler who loses his state thinks his own ministers worthy. How could he knowingly employ the disloyal?” Fang bows: “I fear that as we now look upon antiquity, so will later ages look upon us.”

The slide reads this as hindsight bias: recollections of prior judgments shift toward what actually happened. The emperor judges You and Li by the outcome, missing that they could not have known it. The same passage also carries the curse of knowledge — the informed struggle to imagine what others do not know (Piaget; the manual that only its author can follow). The slide's further list: illusion of control, confirmation bias, neglect of regression to the mean, the affect heuristic; on the hot hand, see Miller & Sanjurjo (2018, Econometrica).

Belief elicitation

slide 32

If beliefs are data, the rule that pays for them matters. The lecture compares two scoring rules.

Quadratic scoring rule

S(q, x) = a − b (x − q)²

A subject reports probability q; the outcome is x ∈ {0, 1}. A risk-neutral subject maximises expected payoff by reporting her true belief p. Risk aversion pulls reports toward 0.5, breaking incentive compatibility.

Binarized scoring rule

Proposed by Hossain & Okui (2013, REStat). Converts the quadratic score into a probability of winning a fixed prize. With only two possible payoffs, reports are robust to risk attitudes.

↩ The link back to Lecture 2

The lecture ties this to the “incentives” norm from Lecture 2: belief data are only as good as the elicitation. The questionnaire's probability items were unincentivized; compare them with incentivized elicitation. This is why the numbers on a survey and the numbers from a paid experiment are not interchangeable evidence.

Prediction markets

slides 33–37

Galton 1907 The ox

In 1906, at a livestock fair in Plymouth, England, Francis Galton recorded about 800 guesses of an ox's dressed weight, made by butchers, farmers and many ordinary visitors. The median guess was 1,207 lb against a true weight of 1,198 lb, an error below 1%. The mean, later computed from his data, was within about 1 lb.

When aggregation works

Judgments are independent, with no common direction of error.

Diverse information

Participants hold different information.

An aggregator

An average or a market price exists and is effective.

When it fails: shared anchors or group opinion make errors compound rather than cancel. The conditions are not decoration — they are the model.

Model 8

When does the crowd cancel?

A simulation of the Galton result. Each judge sees the truth plus noise; slide the number of judges and the size of a shared bias. With independent errors the average converges; a common bias does not average away, and the median inherits it exactly.

Contract design Wolfers & Zitzewitz (2004, JEP)	Applications
A contract pays $1 if event X occurs and 0 otherwise; its price is p. So p ≈ the market's aggregate P(X). Theoretical basis: the efficient market hypothesis, under which prices reflect all available information.	Iowa Electronic Markets: real-money election contracts for academic research. July 2003: the U.S. Department of Defense proposed a Policy Analysis Market, including contracts on terrorist attacks; it was cancelled after widespread criticism. Corporate markets at Google, HP, Microsoft and others forecast project timelines and sales (Cowgill & Zitzewitz, 2015, REStud).

Limits of polls

Non-response: refusers may differ systematically. Social desirability bias: respondents hide unpopular views. Unrepresentative samples: landline vs mobile, education mix. Opinions shift over time; interviewer effects.

Strengths and limits of markets

Traders have incentives to be accurate; prices adjust continuously, pooling dispersed information. Limits: inexperienced traders, noisy prices in thin markets, possible manipulation. Traders themselves are not a representative sample.

The slide closes with a point that undercuts both: beliefs also depend on one's community — even professional analysts largely defer to those around them on most topics. Aggregation cancels independent errors; it does not cancel a shared prior.

▤ The 2020 vote-count screenshots (slide 37)

Two historical screenshots aggregate Betfair and other exchanges during the 2020 U.S. presidential vote count. The candidates' implied win probabilities swing sharply as results come in. The slide labels them illustrations of price updating, not evidence about forecasting accuracy — the workbench keeps that distinction.

Irrational beliefs

slides 38–42

The last movement of the lecture leaves the laboratory. Beliefs can depart from reality by a large margin, and the departure can have consequences. Three 《世说新语》 cases carry the section.

Mars in the Supreme Tenuity 《世说新语 · 言语》

初，荧惑入太微，寻废海西。简文登阼，复入太微，帝恶之。时郗超为中书在直。引超入曰：“天命修短，故非所计，政当无复近日事不？”超曰：“大司马方将外固封疆，内镇社稷，必无若此之虑。臣为陛下以百口保之。”帝因诵庾仲初诗曰：“志士痛朝危，忠臣哀主辱。”声甚凄厉。

Mars had entered the Supreme Tenuity enclosure, and soon the Duke of Haixi was deposed. After Emperor Jianwen took the throne, Mars entered it again, and the emperor was uneasy. He summoned Xi Chao and asked whether “there will be no repeat of recent events”. Xi Chao staked his hundred kin that there would not. The emperor recited: “The resolute grieve at peril to the court; the loyal mourn their lord's disgrace.”

Context, as the slide gives it: from the late Han through the Wei–Jin era, the correspondence of Heaven and humans was widely held, and celestial signs were read as omens. Mars entered the enclosure and a ruler was deposed; when the sign recurred, the emperor feared the same fate. He treated a temporal sequence as a causal one. Normatively, a single co-occurrence supports neither a causal claim nor a forecast.

Guo Pu and the dragon's ear 《世说新语 · 术解》

晋明帝解占冢宅，闻郭璞为人葬，帝微服往看。因问主人：“何以葬龙角？此法当灭族！”主人曰：“郭云：‘此葬龙耳，不出三年，当致天子。’”帝问：“为是出天子邪？”答曰：“非出天子，能致天子问耳。”

Emperor Ming understood the divination of grave sites. Hearing that Guo Pu had sited a burial, he went in disguise and asked the owner, “Why bury on the dragon's horn? That method brings extermination on the clan!” The owner said, “Guo said this is the dragon's ear: within three years it will bring the Son of Heaven.” “Will it produce a Son of Heaven?” “Not produce one, but bring the Son of Heaven here to ask about it.”

The slide's reading is the social use of prophecy: diviners' prophecies are vague enough to fit whatever happens. The late-Han prophecy “he who replaces Han is 当涂高, the tall one by the road” was claimed by Yuan Shu (courtesy name 公路, “public road”), by the Cao Wei court (魏 can mean a tall gate tower), and by Wang Jun (his father was styled 处道, “dwelling on the way”). One prophecy backing rival claims suggests it served to legitimize existing aims, not to inform.

The plum grove 《世说新语 · 假谲》

魏武行役，失汲道，军皆渴，乃令曰：“前有大梅林，饶子，甘酸，可以解渴。”士卒闻之，口皆出水，乘此得及前源。

On campaign, Cao Cao lost the way to water and his army was parched. He announced: “Ahead lies a great plum grove, heavy with fruit, sweet and sour, to quench your thirst.” At this the soldiers' mouths watered, and so they reached a spring ahead.

A belief need not be true to change behavior and physiology. This is the section's bridge from epistemology to economics: beliefs enter utility and action directly, not only through their accuracy.

Evidence	What it shows
Zodiac years and risk taking	Some Chinese investors believe one's zodiac year brings bad luck, and take less risk in that year (Fisman et al., Management Science).
Beliefs that ignore evidence	Some people believe the Earth is flat or that the Moon landings never happened, despite overwhelming evidence.
Motivated beliefs	Beliefs guide decisions but also yield utility directly, e.g. through a positive self-image. Bénabou & Tirole (2002, QJE): confidence offsets weak willpower, so people have reason to sustain inflated self-views. Motivated memory: positive and negative information are recalled asymmetrically (Li, 2012).

Consequences

Confirmation bias: selective search and interpretation deepen polarization. Overconfidence can raise effort and performance, one reason it persists. Belief biases carry real costs in investment, health and education decisions.

Norm violated

Bayes' rule: updating should not depend on whether the conclusion is welcome. A motivated belief is a Bayesian update with the likelihood quietly replaced by what one wants to be true.

? The lecture's own coda

Slides 43–44 restate the whole lecture in parallel prose (骈语). The lines that matter for revision: 「直觉迅捷，每以近似代精算；思虑迟缓，方能校验而纠偏」 — intuition trades calculation for approximation; reflection alone can check it. 「信号虽明，莫忘先验之比率；证据虽新，当循贝氏以更新」 — whatever the signal, remember the base rate; whatever the evidence, update by Bayes. 「信念或随所欲而移，推断当守其规」 — belief may bend toward what we wish, so inference must keep to its rules.

Summary sheet

printable

Two systems

System 1: fast, parallel, automatic, effortless, associative, slow-learning, emotional. System 2: slow, serial, controlled, effortful, rule-governed, flexible, neutral. Correction by System 2 takes effort and is not always engaged.

Attribute substitution

A hard target attribute is judged by an accessible heuristic attribute, and the swap goes unnoticed. Kahneman (2003, p. 1460).

The three heuristics

Representativeness: similarity to a process stands in for probability. Availability: ease of recall stands in for frequency. Anchoring: a starting value stands in for the estimate. Tversky & Kahneman (1974).

The norms they break

Independence · law of large numbers · conjunction rule P(A∧B) ≤ P(A) · Bayes' rule · calibration.

Bayes' rule

Pr(B | D) = Pr(D | B)Pr(B) / Pr(D)

Eddy's screening example: 1% prevalence, 90% sensitivity, 10% false positive → posterior ≈ 8.3%; natural frequencies give 9 of 108.

Compound events

Lotto 6/49 = 1 / 13,983,816

Birthday problem, n = 30: no shared birthday ≈ 29.4%, so at least one shared ≈ 70.6%. Conjunctions overestimated, disjunctions underestimated.

Overconfidence · three forms

Overestimation of absolute performance · overplacement in relative rank · overprecision in interval width. Moore & Healy (2008). About 50% of true values fall outside stated 90% intervals.

Scoring rules

Quadratic: S(q, x) = a − b(x − q)²

Truthful for a risk-neutral subject; risk aversion pulls toward 0.5. Binarized scoring rule (Hossain & Okui, 2013) is robust to risk attitudes.

Wisdom of crowds

Galton's ox: about 800 guesses, median 1,207 lb against a true 1,198 lb; mean within about 1 lb. Works when judgments are independent, information is dispersed and an aggregator exists. Shared anchors make errors compound.

The lecture's verdict

Heuristics are usually useful — that is why they survive. They fail systematically, and the direction of the failure is what a theory can predict.

Key concepts

English term · 中文

Term	中文	Meaning in this lecture
System 1 / System 2	系统一 / 系统二	Fast, automatic intuition vs slow, controlled reasoning.
Attribute substitution	属性替代	Answering a hard question by answering an easier, related one without noticing.
Heuristic	启发式	A simple rule that reduces a complex judgment to a simpler operation.
Representativeness	代表性	Judging probability by similarity to the generating process.
Law of small numbers	小数定律	Expecting small samples to resemble the population too closely.
Gambler's fallacy	赌徒谬误	Expecting independent deviations to correct themselves in the short run.
Conjunction fallacy	合取谬误	Judging P(A∧B) > P(A), as in the Linda problem.
Base-rate neglect	基率忽视	Letting the likelihood dominate the prior; the rare disease with many false positives.
Natural frequencies	自然频率	Expressing the same Bayes problem as counts out of 1,000, which people handle better.
Availability	可得性	Judging frequency by ease of recall.
Anchoring	锚定	Adjusting insufficiently from an irrelevant starting value.
Conjunctive / disjunctive event	合取事件 / 析取事件	A conjunction of steps is overestimated; a disjunction is underestimated.
Overestimation / overplacement / overprecision	高估 / 高定位 / 过度精确	The three forms of overconfidence (Moore & Healy, 2008).
Calibration	校准	Stated confidence matches hit rates; 90% intervals should contain 90% of truths.
Hindsight bias	后见之明偏差	Recollections of prior judgments shift toward what happened.
Curse of knowledge	知识的诅咒	The informed cannot imagine not knowing.
Quadratic scoring rule	二次评分规则	Pays S = a − b(x − q)²; truthful under risk neutrality.
Binarized scoring rule	二值化评分规则	Converts the score into a win probability; robust to risk attitudes.
Prediction market	预测市场	A contract price p approximating the market's aggregate P(X).
Motivated belief	动机性信念	Belief shaped by the utility of holding it, not only by evidence.

Self-check

graded, with explanations

0 / 0 correct

The two systems and substitution

Q1The bat and ball cost $11; the bat costs $10 more than the ball. What is the bat's price, and which system produces the tempting wrong answer?

Correct.Set x + y = 11 and x − y = 10; then x = 10.50, y = 0.50. System 1 substitutes “$10 more” with “$10” and checks only the sum. The failure is not arithmetic — it is checking one constraint instead of both.

Not quite.The intuitive answer $10 satisfies x + y = 11 but fails x − y = 10. The correct price is $10.50, and the reason is that both constraints must hold at once.

Q2What is attribute substitution, as Kahneman defines it?

Correct.The three elements are all needed: the target is inaccessible, the proxy is accessible, and the swap goes unnoticed by System 2. Drop the last element and it becomes a description of deliberate simplification, not a bias.

Not quite.Attribute substitution is about which attribute is judged, not which lottery is chosen. The definition requires a hard target, an accessible proxy, and an undetected swap.

Probability and updating

Q3A disease has prevalence 1%. A test has sensitivity 90% and false-positive rate 10%. A person tests positive. Roughly what is the probability of disease?

Correct.(0.9 × 0.01) / (0.9 × 0.01 + 0.1 × 0.99) = 0.009 / 0.108 ≈ 8.3%. In counts: 10 sick, 9 test positive; 990 healthy, 99 test positive; 9 of 108 positives are true. The base rate dominates because the disease is rare.

Not quite.Sensitivity is P(positive | sick), not P(sick | positive). The prevalence is 1%, so most positives come from the large healthy group. Work it out in counts: 9 true positives, 99 false positives.

Q4Linda is described as bright, outspoken, a philosophy major and active in social justice. Most respondents say “bank teller and feminist” is more probable than “bank teller”. Which norm does this violate?

Correct.A conjunction is a subset of each of its parts, so it cannot be more probable. The stereotype makes B representative, and similarity overrides the set-theoretic constraint. Base rates may also matter, but the violated rule is the conjunction rule.

Not quite.The direct violation is set-theoretic: “bank teller and feminist” is contained in “bank teller”, so it cannot be more likely. That is the conjunction rule.

Q5Which condition is not one the lecture gives for the wisdom of crowds to work?

Correct.Galton's crowd contained butchers, farmers and ordinary visitors; individual accuracy was not the point. Independent errors cancel in the aggregate even when individuals are noisy — provided the errors do not share a direction. Shared anchors make them compound instead.

Not quite.The three conditions are independence, dispersed information and an aggregator. Individual calibration is not required; shared bias is what breaks the result.

Overconfidence and beliefs

Q6A student says she is “certain” her 90% confidence interval for the Amazon's length is right, but the true value falls outside it. Which form of overconfidence is this?

Correct.The interval is the object being judged. A 90% interval should miss about 10% of the time; in the data, about 50% of true values fall outside. Overestimation is about absolute performance and overplacement about relative rank; neither is defined by interval width.

Not quite.The failure is in the interval, not in a predicted score or a claimed rank. Too-narrow intervals are overprecision.

Q7Explain why the quadratic scoring rule elicits truthful reports from a risk-neutral subject, and why risk aversion breaks that conclusion.

Set-up. The subject reports q; the outcome is x ∈ {0, 1}; the payoff is S(q, x) = a − b(x − q)². Let her true belief be p = Pr(x = 1).

Expected payoff. E[S] = a − b[p(1 − q)² + (1 − p)q²]. Differentiate with respect to q: dE[S]/dq = 2b[(1 − q)p − q(1 − p)] = 2b(p − q). The derivative is zero exactly at q = p, and the second derivative is negative, so this is a maximum. The slope b does not affect the location, only the steepness — which is why the rule is incentive-compatible for a risk-neutral subject.

Why risk aversion breaks it. A risk-averse subject does not maximise the expectation of a convex payoff. The realised score is higher when q is close to the outcome and lower otherwise; reporting an extreme q makes the payoff more variable. Moving q toward 0.5 reduces that variability, so a risk-averse subject trades some expected score for a less variable one. The optimal report is pulled toward 0.5, and the gap grows with risk aversion.

The fix. The binarized scoring rule converts the score into a probability of winning a fixed prize. With only two possible payoffs, the subject's risk attitude affects both branches symmetrically and cancels from the comparison, so the truthful report survives (Hossain & Okui, 2013).

Lecture 4

Risk

Source: lecture 4 risk.pptx — 58 slides Expected utility → prospect theory → cumulative prospect theory Mostly equations on image-led slides

This is the technical centre of the course's first half, and it is built as a sequence of failures. Start with expected value: the St Petersburg game has infinite expected value and nobody will pay a large sum for it, so value must be curved. That gives expected utility. Expected utility then imposes axioms — completeness, continuity, independence — and the axioms make sharp predictions that people violate in repeatable ways. Prospect theory is the repair: value is defined over gains and losses relative to a reference point, the value function is concave in gains and convex in losses, losses loom larger, and probabilities are replaced by decision weights. The 1992 cumulative version fixes the 1979 version's violation of stochastic dominance.

The deck is equation-heavy and many slides carry only a title in the text layer. Every formula below was read off the rendered slide, including the numerical example from Tversky & Kahneman (1992). Where the deck's algebra has a slip, the workbench flags it rather than reproducing it — see the note on subadditivity in §8.

This lecture overlaps the prospect-theory model already built for Lecture 1. That model stays where it is and is linked from here; the two new figures in this lecture do different jobs: the St Petersburg price, and the cumulative weighting of a six-outcome gamble.

Concept map

from a paradox to a functional form

The problemHow should a lottery be valued?

first answer, and why it fails

Expected valueProbability-weighted money. Infinite for the St Petersburg game.

St PetersburgEV = +∞, willingness to pay is small.

Expected utilityU(l) = Σ pᵢu(xᵢ). A concave u turns the infinite series into a finite number.

what expected utility assumes

AxiomsCompleteness, continuity, independence.

TheoremThe axioms deliver an expected-utility representation.

Three tenetsAsset integration · risk aversion · expectation.

Dutch bookViolating independence exposes you to a sure loss.

the violations that force a new theory

Reference dependenceGains and losses, not final wealth.

Reflection effectRisk averse in gains, risk seeking in losses.

Common ratioSame probability ratio, different choice.

Allais paradoxCertainty effect.

Lottery and insuranceOverweighting small probabilities.

the repair

Value functionv(x) = x^α in gains; −λ(−x)^β in losses.

Probability weightingπ(p), not p: subproportional, subcertain, overweighting small p, subadditive.

CPT 1992Rank outcomes, weight decumulative events, evaluate gains and losses separately.

From expected value to expected utility

slides 6–10

A lottery: l = (x, p; y, 1 − p) — x occurs with probability p, y with probability 1 − p.

Expected utility: U(l) = p u(x) + (1 − p) u(y)

U is the utility function over lotteries; u is the utility over outcomes (money). The preference over lotteries depends only on u — the deck underlines this because it is what makes the whole construction testable.

Paradox St Petersburg

A fair coin is tossed until the first head. If it happens on the n-th trial, you win 2ⁿ dollars. What is your willingness to pay to play?

EV = (1/2)·2 + (1/4)·4 + (1/8)·8 + … = 1 + 1 + 1 + … = +∞

You will not pay a large amount for the game.
So expected value is not a good measure of utility.
With u(x) = ln x: U = Σ (1/2ⁿ) ln(2ⁿ) = ln 2 · Σ n/2ⁿ = 2 ln 2 ≈ 1.39.
The utility is finite with a concave u(x).

The deck's own note gives the series trick: use Σ xⁿ = 1/(1 − x) for |x| < 1, differentiate with respect to x, and set x = 1/2; the sum is 2.

Model 9

What is the St Petersburg game worth?

Set the curvature of the utility function and the number of tosses the game is allowed. The truncated expected value grows without bound; the certainty equivalent does not — except at the linear-utility boundary, where the paradox returns.

Example The same lottery, twice

l = ($100, 0.5; 0, 0.5). The mean of the lottery is $50. Let u(x) = x^0.5.

Expected utility of the lottery: U(l) = 0.5(100^0.5) + 0.5(0^0.5) = 5.
Utility of the sure $50: U(50) = u(50) = 50^0.5 ≈ 7.07.
U(50) > U(l), so the decision maker prefers $50 over the lottery.

Risk aversion is exactly this ordering: the mean of the gamble is preferred to the gamble.

Risk averse

Prefers the mean of the gamble over the gamble. Equivalently, u(ax + (1 − a)y) ≥ a u(x) + (1 − a)u(y) for all x, y and a ∈ [0,1]; equivalently u″(x) ≤ 0.

Risk neutral

Indifferent between the mean of the gamble and the gamble.

Risk seeking

Prefers the gamble over the mean of the gamble.

Measuring risk attitudes

slides 11–17

Instrument	How it works	What it measures
Balloon / bomb risk task	Pump a balloon for money; each pump raises the prize and the chance of a burst. The linked videos are on the slide.	Revealed willingness to take an incremental risk.
Self-report	“Rate your willingness to take risks in general” on a 10-point scale, 1 = completely unwilling, 10 = completely willing.	Stated general risk attitude.
Domain-specific scale Weber et al. (2002)	Rate on a 5-point scale how likely you would be to do a particular behaviour, such as “Drinking heavily at a social function” or “Gambling a week's income at a casino”.	Risk attitude by domain — the scale that challenges the universal-attitude assumption.
Investment game Gneezy & Potters (1997)	Endowment of 100 cents. Choose x to invest in a risky asset that returns 2.5x with probability one-half and nothing with probability one-half; keep 100 − x.	The amount invested is the measure of risk preference.
Multiple price list Holt & Laury (2002)	Ten paired decisions. Use the switch point from Option A to Option B as the measure; the slide's warning is the multiple switching points problem — a complex task generates confusion and forced choices.	Risk attitude from a single switch point, mapped to a CRRA range.

▤ The MPL numbers, from the slide's notes

Holt & Laury's list: Option A pays $2 with probability i/10 and $1.60 otherwise; Option B pays $3.85 with probability i/10 and $0.10 otherwise. In the first row the expected value of A exceeds B by $1.17. A switch at 4 A / 6 B is consistent with risk neutrality, with a CRRA coefficient in (−0.15, 0.15); 6 A / 4 B implies risk aversion, with CRRA in (0.41, 0.68).

Card task A worked MPL

Option A: a 50% chance of $60 and a 50% chance of $0. Option B: a sure amount, listed in ascending order: $15, $19, $23, $25, $27, $29, $30, $31, $33, $35. Tick A or B in each row.

If you switch from A to B at $30, you accept the sure amount as soon as it reaches the gamble's expected value ($30).
Switching later means you kept the gamble when its expected value exceeded the sure amount — risk seeking.
Switching earlier means you gave up expected value for certainty — risk aversion.

The switch point is the measurement. The slide's own question — switching point to risk attitude? — is answered by the direction: a later switch means more risk taking.

? Risk attitudes across the life course (slide 15)

The slide plots stated risk attitude against age from about 20 to 80, separately for men (solid) and women (dashed), with confidence bands. The pattern is a steady decline with age, and men above women at every age shown. The slide gives no source line for the figure, so the workbench records the shape and does not attach a citation the deck does not supply.

Huan Wen at the gaming board 《世说新语 · 任诞》

桓宣武少家贫，戏大输，债主敦求甚切，思自振之方，莫知所出。陈郡袁耽，俊迈多能。宣武欲求救于耽，耽时居艰，恐致疑，试以告焉。应声便许，略无慊吝。遂变服怀布帽随温去，与债主戏。耽素有艺名，债主就局曰：“汝故当不办作袁彦道邪？”遂共戏。十万一掷，直上百万数。投马绝叫，傍若无人，探布帽掷对人曰：“汝竟识袁彦道不？”

Huan Wen, young and poor, loses heavily at chaupar. Yuan Tan, in mourning, agrees at once to help, changes clothes, hides his mourning cap, and goes to the creditor's table. The creditor doubts he can play like Yuan Tan. They play at a hundred thousand a throw, soon into the millions; Yuan Tan shouts as though alone, then throws the cap in his opponent's face: “Now do you recognize Yuan Tan?”

The second story on the slide: Xie Xuan, as a boy, loved a purple silk sachet; his uncle Xie An gambled with him for it and burned it the moment he won (假谲). The lecture uses both to make a single point about gambling as a domain where risk attitude is observable — and about the confidence with which observers read character from it.

Why Liu Tan believed Huan Wen could take Shu 《世说新语 · 识鉴》

桓公将伐蜀，在事诸贤，咸以李势在蜀既久，承藉累叶，且形据上流，三峡未易可克。唯刘尹云：“伊必能克蜀。观其蒲博，不必得，则不为。”

When Huan Wen was about to attack Shu, every worthy in the administration argued that Li Shi had held Shu for generations, occupied the upper reaches, and that the Three Gorges would not be easy. Only Liu Tan said: “He will certainly take Shu. I have watched his gambling: if he is not sure to win, he does not play.” (The slide glosses 蒲博: 樗蒲 chūpú, a gambling game.)

The slide's remarks make the methodological assumption explicit: gambling is a useful tool to measure risk attitude, and the implicit assumption is that risk attitude is stable across domains — hence behaviour in one domain can predict behaviour in another. That assumption is exactly what the domain-specific scale above calls into question. The story is not evidence for the assumption; it is an ancient statement of it.

First-order dominance and the axioms

slides 18–24

FOSD First-order stochastic dominance

Distribution F(·) yields unambiguously higher returns than G(·) (MWG 6.D). For every amount x, the probability of getting at least x is higher under F: F(x) ≤ G(x) for every x. This is equivalent to the criterion that every EU maximiser who values more over less prefers F to G.

Lottery X	Lottery Y
0.4, $10	0.5, $12
0.6, $3	0.5, $3

P(X > 1) = 1 ≤ P(Y > 1) = 1 · P(X > 3) = 0.4 ≤ P(Y > 3) = 0.5 · P(X > 10) = 0 ≤ P(Y > 10) = 0.5

Y first-order dominates X. Every expected-utility maximiser who prefers more money to less must choose Y — without any assumption about the shape of u.

Completeness and transitivity

The ranking exists and is consistent — the same two axioms as Lecture 2, now applied to lotteries.

Continuity

≽ on the simple lottery space ℒ is continuous if, for any L, L′, L″ ∈ ℒ, the sets {α ∈ [0,1]: αL + (1 − α)L′ ≽ L″} and {α ∈ [0,1]: L″ ≽ αL + (1 − α)L′} are closed. In words: small changes in probabilities do not change the nature of the ordering.

Independence

For all lotteries P, Q, R ∈ ℒ and every α ∈ (0,1): P ≽ Q iff αP + (1 − α)R ≽ αQ + (1 − α)R. Mixing each of two lotteries with a third leaves the ordering of the mixtures independent of the third.

Expected utility theorem

If the rational preference relation ≽ on ℒ satisfies continuity and independence, a utility function U: ℒ → ℝ with the expected-utility form represents ≽. That is, numbers uₙ can be assigned to outcomes so that for any two lotteries L = (p₁, …, p_N) and L′ = (p′₁, …, p′_N):

L ≽ L′ iff Σ uₙpₙ ≥ Σ uₙp′ₙ

Example Independence, in numbers

If (50, 1) ≽ (100, 0.5; 0, 0.5), independence implies (50, 0.02; 0, 0.98) ≽ (100, 0.01; 0, 0.99).

α = 0.02, 1 − α = 0.98, R = (50, 0; 0, 1)
αP + (1 − α)R = (50, 0.02; 0, 0.98)
αQ + (1 − α)R = (100, 0.01; 0, 0.99)

The slide's question is direct: is your choice consistent with independence? If you chose the sure $50 at the first pair and then switched to the 1% shot at $100 in the second, you violated it.

Dutch book Why the axioms have teeth

Assume L₁ ≻ L₂ but αL + (1 − α)L₂ ≻ αL + (1 − α)L₁. A merchant M can set up an arbitrage for the decision maker DM.

DM takes αL + (1 − α)L₁ — a contingency with random event E, which both agree has probability (1 − α) — while M holds αL + (1 − α)L₂.
M gives αL + (1 − α)L₂ to DM and takes some money.
M now lets DM agree to replace L₂ with L₁ in case E occurs, and takes more money.
Now DM again holds αL + (1 − α)L₁, M holds αL + (1 − α)L₂, and M has money.
Repeat …

The point is not that merchants actually do this. It is that a preference order admitting the cycle is one at which a sure loss can be constructed — the same argument as the Dutch book for transitivity in Lecture 2.

The three tenets of expected utility

slides 25–27

Asset integration

A prospect (x₁, p₁; …; xₙ, pₙ) is acceptable at asset w iff U(w + x₁, p₁; …; w + xₙ, pₙ) ≥ u(w). Outcomes are merged with the existing portfolio.

Risk aversion

u is concave.

Expectation

U(x₁, p₁; …; xₙ, pₙ) = p₁u(x₁) + … + pₙu(xₙ)

The value is the probability-weighted average of outcome utilities.

Test Asset integration fails

Case 1. In addition to whatever you own, you have been given 1,000. You choose between A1: (1,000, 0.5) and B1: (500).
Case 2. In addition to whatever you own, you have been given 2,000. You choose between A2: (−1,000, 0.5) and B2: (−500).

Most people choose B1 ≻ A1 — the sure 500.
Most people choose A2 ≻ B2 — the gamble.

Under asset integration the two cases are the same problem: U(A1) = 0.5u(w + 2000) + 0.5u(w + 1000), U(B1) = u(w + 1500), U(A2) = 0.5u(w + 1000) + 0.5u(w + 2000), U(B2) = u(w + 1500). A1 and A2 have the same expected utility, B1 and B2 have the same expected utility, so the same choice should appear in both cases. It does not.

Reference dependence

slides 28–34

The repair begins by rejecting asset integration. The decision maker separates gain and loss relative to a reference point, without merging them into final wealth.

U(A1) = 0.5u(1000) + 0.5u(0) · U(B1) = u(500)
U(A2) = 0.5u(0) + 0.5u(−1000) · U(B2) = u(−500)

With this coding, both B1 ≻ A1 and A2 ≻ B2 can hold for some u function. The reference point is doing the work that final wealth was supposed to do.

Perception Two squares, one grey

The slide shows two grey squares, one on a black background and one on a light background. They are the same luminance; the surround changes what you see.

Then the water bowls: ice water in the left bowl, hot water in the right, room temperature in the middle. Immerse the left hand and the right hand, then dip both into the middle bowl. The same water feels cold to one hand and warm to the other.

The analogy is exact: sensation and valuation depend on the reference point, not on the absolute level. This is why the deck introduces reference dependence with perceptual examples before any economics.

Reflection Risk aversion and risk seeking

Choose between A1: (3,000) and B1: (4,000, 0.8). Then choose between A2: (−3,000) and B2: (−4,000, 0.8).

Most people choose A1 ≻ B1: risk averse in the gain domain.
Most people choose B2 ≻ A2: risk seeking in the loss domain.
This is not consistent with the usual assumption of risk aversion everywhere.

The reflection effect: the same probabilities and the same magnitudes, with signs reversed, produce the opposite attitude toward risk.

Loss aversion The 50/50 gamble at zero

Choose between A1: 0 and B1: (−100, 0.5; 100, 0.5).

Most people choose A1 ≻ B1 — risk averse across the gain and loss domain.
0.5u(100) + 0.5u(−100) < u(0) = 0.
Hence u(100) < −u(−100).

Loss looms larger than gain. The disutility of losing 100 exceeds the utility of winning 100.

The value function

slides 32, 35–36

Gain/loss

Value is defined relative to the reference point, not over final wealth.

Diminishing sensitivity

Concave in gains, convex in losses: u″(x) < 0 for x > 0; u″(x) > 0 for x < 0.

Loss aversion

Losses loom larger than gains. The loss branch is steeper.

▤ Diminishing sensitivity is a perceptual law first

The slide anchors it in the Weber–Fechner law: turning on a weak light in a dark room is noticed; the same light in a bright room is not. In value terms, the difference between getting 900 and 1,000 is smaller than the difference between getting 100 and 200. The same curvature appears on both sides of the reference point, with the sign of the second derivative flipped.

v(x) = (x − r)^α for x ≥ r · v(x) = −λ(r − x)^β for x < r

Tversky & Kahneman's (1992) estimates: λ = 2.25, α = β = 0.88. The figure is the familiar S-shape: concave above the reference point, convex below, steeper below.

2×2 The fourfold pattern of risk attitudes

	High or intermediate probability	Low probability
Gains	Risk averse Salary	Risk seeking Buying lottery
Losses	Risk seeking Facing a fine	Risk averse Buying insurance

The pattern needs both pieces of prospect theory. The value function supplies the gain/loss asymmetry; the weighting function supplies the small-probability overweighting that flips the low-probability cells.

Probability weighting

slides 37–48

Common ratio Problems 7 and 8

It is commonly observed that
(3000, 0.90) ≻ (6000, 0.45)
(6000, 0.001) ≻ (3000, 0.002)

EU of the first: 0.90u(3000) > 0.45u(6000) ⇒ u(3000)/u(6000) > 0.5
EU of the second: 0.001u(6000) > 0.002u(3000) ⇒ u(3000)/u(6000) < 0.5

Contradiction. The ratio is required to be both above and below 0.5. The pattern violates independence — not the curvature of u.

Derivation The condition on π(p)

Take P = (3000, 0.90), Q = (6000, 0.45), R = 0 and α = 2/900. Then αP + (1 − α)R = (3000, 0.002) and αQ + (1 − α)R = (6000, 0.001).

π(0.90)u(3000) > π(0.45)u(6000) and π(0.001)u(6000) > π(0.002)u(3000)
⇒ π(0.45)/π(0.90) < u(3000)/u(6000) < π(0.001)/π(0.002)

Subproportionality: a common ratio applied to two probabilities does not scale the decision weights proportionally. This is the property the 1979 weighting function was built to capture.

Allais The certainty effect

It is commonly observed that
2400 ≻ (2500, 0.33; 2400, 0.66; 0, 0.01)
(2500, 0.33) ≻ (2400, 0.34)

u(2400) > 0.33u(2500) + 0.66u(2400) ⇒ 0.34u(2400) > 0.33u(2500)
but the second choice requires 0.33u(2500) > 0.34u(2400)

Contradiction. In terms of weights: π(0.66) + π(0.34) < 1 — subcertainty. The weights on a pair of complementary events sum to less than one, because certainty is weighted at 1 while near-certainty is discounted.

Lottery

Buying a lottery: (5000, 0.001) ≻ (5). Expected utility: 0.001u(5000) > u(5), so u(5)/u(5000) < 0.001. But if u is concave for x > 0, u(5)/u(5000) > 0.001 — a contradiction. Repair: π(0.001) > 0.001, overweighting small p.

Insurance

Paying 5 to avoid a 0.1% chance of losing 5,000: (−5) ≻ (−5000, 0.001). The same overweighting of the small probability explains why both the lottery ticket and the insurance premium can be bought by the same person — in gains and losses respectively.

Subadditivity Small probabilities, split and unsplit

It is commonly observed that (0.001, 6000) ≻ (0.002, 3000). Expected utility would require u(3000)/u(6000) < 0.5, but concavity gives u(3000)/u(6000) > 0.5 — contradiction. With weights: π(0.001)/π(0.002) > 1/2.

! A slip on the slide, flagged

Slide 47 defines subadditivity as π(rp) > rπ(rp) for 0 < r < 1. That is not the condition the derivation above establishes, and it cannot be: the right-hand side is r times the left-hand side, so it says π(rp) > rπ(rp), which is true for any positive weight whenever r < 1 and has nothing to do with subadditivity. The standard condition — and the one the slide's own numbers imply — is π(rp) > rπ(p). The workbench states the corrected form rather than reproducing the typo silently.

Properties Four restrictions on π(·)

Property	Statement	Source in the deck
Subproportionality	π(0.45)/π(0.90) < u(3000)/u(6000) < π(0.001)/π(0.002)	Common ratio, slide 41
Subcertainty	π(0.66) + π(0.34) < 1	Allais, slide 43
Overweighting small p	π(p) > p	Lottery, slide 45
Subadditivity for small p	π(0.001)/π(0.002) > 1/2	Slide 47

An intuitive way to keep them together: the weighting function is shallow in the middle and steep at the ends. It crosses the 45° line in the interior, overweights small probabilities, and underweights moderate-to-large ones — which is why a 90% chance is not treated as nine times a 10% chance.

Prospect theory in 1979, cumulative in 1992

slides 49–58

1979 · Two phases

Editing phase: coding, combination, cancellation, simplification, detection of dominance.
Evaluation phase: valuation and probability weighting.

1979 · Two limits

The theory is written for 2 or 3 outcomes, and its extension to N outcomes can violate stochastic dominance. It also leaves open how to determine the reference point.

1992 The cumulative repair

Rank the lottery outcomes from the worst x₁ to the best xₙ. From x₁ to x_L is loss; from x_{L+1} to xₙ is gain. There can be a separate weighting function for gains and losses.

w_g is a function on the decumulative events X ≥ xᵢ.
For gains: πᵢ = w_g(pᵢ + … + pₙ) − w_g(p_{i+1} + … + pₙ)
For losses: πᵢ = w_l(p₁ + … + pᵢ) − w_l(p₁ + … + p_{i−1})

w_g(p) = p^r / ((p^r + (1 − p)^r)^1/r) · w_l(p) = p^δ / ((p^δ + (1 − p)^δ)^1/δ)

In empirical work, w_g and w_l are usually taken to be the same. The slide's estimates: λ = 2.25, α = β = 0.88, γ = 0.61, δ = 0.69, from 25 graduate students at Berkeley and Stanford. Prelec's (1998) alternative: w(p) = exp(−(−ln p)^α).

Model 10

A six-outcome gamble, weighted cumulatively

The die gamble from Tversky & Kahneman's (1992) numerical example: roll a die; an even result pays the face value in dollars, an odd result costs the face value. Set the curvature, loss aversion and the two weighting parameters; the bars are the cumulative decision weights on each of the six outcomes. At the 1992 estimates the gain side is discounted and the loss side is priced more steeply.

Numbers The 1992 die example, spelled out

Outcomes are equiprobable at 1/6: f⁺ = (0, 1/2; 2, 1/6; 4, 1/6; 6, 1/6), f⁻ = (−5, 1/6; −3, 1/6; −1, 1/6; 0, 1/2). Then V(f) = V(f⁺) + V(f⁻), where

V(f) = v(2)[w⁺(1/2) − w⁺(1/3)] + v(4)[w⁺(1/3) − w⁺(1/6)] + v(6)[w⁺(1/6) − w⁺(0)]
+ v(−5)[w⁻(1/6) − w⁻(0)] + v(−3)[w⁻(1/3) − w⁻(1/6)] + v(−1)[w⁻(1/2) − w⁻(1/3)]

The weights are differences of cumulative weights, which is what keeps the transformed weights summing to one and preserves stochastic dominance.

? Why the cumulative form is necessary

The slide's argument: U(l) = π(p)u(x) + π(q)u(y) violates stochastic dominance unless π is additive. If π is additive — π(p + q) = π(p) + π(q) whenever p + q ≤ 1 — then π(p) = p for all p, which is expected utility. So any genuinely non-linear weighting must be non-additive, and the simple form then misprices the same lottery depending on how it is written. Cumulative weighting removes the problem by assigning each outcome the difference between two cumulative weights: the same lottery written two ways gets the same value.

Summary sheet

printable

Lottery and expected utility

l = (x, p; y, 1 − p)

U(l) = p u(x) + (1 − p)u(y). U is over lotteries; u is over outcomes.

St Petersburg

EV = Σ (1/2ⁿ)·2ⁿ = +∞

With u = ln x, U = 2 ln 2 ≈ 1.39. The certainty equivalent is about $4; concavity makes the price finite.

Risk aversion

Prefers the mean over the gamble; u concave; u(ax + (1−a)y) ≥ au(x) + (1−a)u(y).

The three axioms

Completeness and transitivity · continuity · independence (P ≽ Q iff αP + (1−α)R ≽ αQ + (1−α)R).

EU theorem

L ≽ L′ iff Σ uₙpₙ ≥ Σ uₙp′ₙ

Continuity + independence + rationality deliver the representation.

Three tenets, and the one that fails

Asset integration, risk aversion, expectation. Asset integration is rejected by the 1,000/2,000 experiment: B1 ≻ A1 and A2 ≻ B2 cannot both hold if outcomes are merged with wealth.

Reference dependence

Gains and losses relative to a reference point. Evidence: the contrast illusion, the water bowls, the reflection effect, and loss aversion.

Value function

v(x) = (x−r)^α · −λ(r−x)^β

λ = 2.25, α = β = 0.88 (Tversky & Kahneman, 1992). Concave in gains, convex in losses, steeper in losses.

Fourfold pattern

Gains: risk averse at high/intermediate p, risk seeking at low p. Losses: risk seeking at high/intermediate p, risk averse at low p.

Weighting properties

Subproportionality · subcertainty (π(0.66)+π(0.34)<1) · overweighting small p (π(p)>p) · subadditivity (π(rp)>rπ(p)).

Common ratio

(3000,0.90) ≻ (6000,0.45) and (6000,0.001) ≻ (3000,0.002)

The two choices require u(3000)/u(6000) to be both above and below 0.5. Breaks independence, not curvature.

Allais / certainty effect

π(0.66) + π(0.34) < 1

Certainty is weighted at 1 while near-certainty is discounted.

CPT 1992

πᵢ = w(pᵢ + … + pₙ) − w(p_{i+1} + … + pₙ)

Rank outcomes; weight decumulative gains and cumulative losses; separate w_g and w_l; estimates λ = 2.25, α = β = 0.88, γ = 0.61, δ = 0.69.

Prelec's weighting function

w(p) = exp(−(−ln p)^α)

An alternative to the Tversky–Kahneman functional form, used widely in empirical work.

Key concepts

English term · 中文

Term	中文	Meaning in this lecture
Lottery	彩票 · 抽彩	A list of outcomes with probabilities, l = (x, p; y, 1 − p).
Expected value	期望值	Probability-weighted money; +∞ for St Petersburg.
Expected utility	期望效用	U(l) = Σ pᵢu(xᵢ); replaces money by its utility.
Certainty equivalent	确定性等值	The sure amount that gives the same utility as the gamble.
Risk aversion	风险厌恶	Prefers the mean to the gamble; u concave.
First-order stochastic dominance	一阶随机占优	F(x) ≤ G(x) for every x; every EU maximiser prefers F.
Independence axiom	独立性公理	Mixing two lotteries with a common third does not reverse their order.
Dutch book	荷兰赌	An arbitrage constructed against a preference order that violates the axiom.
Asset integration	资产整合	Merging a prospect with existing wealth; the tenet the evidence rejects.
Reference dependence	参照点依赖	Value is defined relative to a reference point, in gains and losses.
Reflection effect	反射效应	Risk averse in gains, risk seeking in losses, same magnitudes.
Loss aversion	损失厌恶	Losses loom larger than gains; λ ≈ 2.25.
Diminishing sensitivity	敏感性递减	Concave in gains, convex in losses; Weber–Fechner.
Fourfold pattern	四重模式	Risk attitude by domain and probability level.
Probability weighting	概率权重	Decision weight π(p) replaces objective p.
Common ratio effect	共同比率效应	Scaling both probabilities by a common factor reverses the choice.
Certainty effect	确定性效应	Certain outcomes are overweighted; Allais paradox.
Subcertainty	次确定性	π(p) + π(1 − p) < 1.
Subproportionality	次比例性	A common probability ratio is not preserved by π.
Subadditivity	次可加性	π(rp) > rπ(p) for small p.
Editing / evaluation phase	编辑阶段 / 评价阶段	The two phases of prospect theory 1979.
Cumulative prospect theory	累积前景理论	The 1992 rank-dependent version, which restores stochastic dominance.

Self-check

graded, with explanations

0 / 0 correct

Expected utility

Q1Why does the St Petersburg game have infinite expected value but a small willingness to pay?

Correct.Each term of the EV series is (1/2ⁿ)·2ⁿ = 1, so the sum diverges. With u = ln x the terms become (n ln 2)/2ⁿ, which sum to 2 ln 2 ≈ 1.39. Concavity is what makes the price finite.

Not quite.The probabilities do sum to one and the game is fair in expected value. The resolution is the curvature of the utility function: the large prizes carry little extra utility.

Q2Most people choose B1 ≻ A1 in the gain framing and A2 ≻ B2 in the loss framing of the 1,000/2,000 experiment. What does this show?

Correct.Under asset integration, U(A1) = 0.5u(w+2000) + 0.5u(w+1000) = U(A2), and U(B1) = u(w+1500) = U(B2). So the same ordering should appear in both cases. The reversal is the evidence against asset integration and for reference dependence.

Not quite.Once you add the endowment to wealth, the two cases have identical utility expressions. The fact that choices reverse is exactly what expected utility with asset integration cannot explain.

Q3The common-ratio pattern (3000, 0.90) ≻ (6000, 0.45) and (6000, 0.001) ≻ (3000, 0.002) violates which axiom?

Correct.The two lotteries in each pair have the same probability ratio (0.90/0.45 = 2 and 0.002/0.001 = 2), yet the choice reverses. Independence says mixing both with a common third lottery cannot reverse their order; here it does.

Not quite.There is no cycle and no missing ranking; the choice is complete and transitive. What fails is the axiom that a common mixing lottery should not change the order — independence.

Prospect theory

Q4Which statement captures loss aversion?

Correct.The 0-vs-(−100,0.5;100,0.5) choice gives 0.5u(100) + 0.5u(−100) < u(0) = 0, hence u(100) < −u(−100). A is the reflection effect, B is probability weighting, C is diminishing sensitivity.

Not quite.Loss aversion is specifically the asymmetry in steepness between the two branches, not curvature and not probability weighting.

Q5Why does cumulative prospect theory weight differences of cumulative probabilities rather than each pᵢ separately?

Correct.The 1979 form can rank a lottery above another that dominates it. The cumulative construction assigns weights by rank and takes differences, so the weights still sum to one and a first-order-dominating lottery cannot be preferred.

Not quite.The goal is to keep the weights coherent. The simple form is not additive; cumulative weighting restores additivity across the rank and preserves first-order stochastic dominance.

Q6In the fourfold pattern, what is the predicted attitude toward a low-probability loss, such as a 0.1% chance of a large accident?

Correct.Losses in the low-probability cell are the insurance quadrant: the small chance is overweighted, so paying a premium to remove it is attractive. High-probability losses are the risk-seeking cell (facing a fine).

Not quite.The four cells are: gains high p — risk averse; gains low p — risk seeking; losses high p — risk seeking; losses low p — risk averse.

Q7Derive the common-ratio contradiction in expected utility step by step, and state the condition on π(p) that the data require.

The data. Most subjects choose (3000, 0.90) ≻ (6000, 0.45) and (6000, 0.001) ≻ (3000, 0.002).

Under EU. Write r = u(3000)/u(6000). The first choice requires 0.90 u(3000) > 0.45 u(6000), i.e. r > 0.45/0.90 = 0.5. The second requires 0.001 u(6000) > 0.002 u(3000), i.e. r < 0.001/0.002 = 0.5. No r satisfies both.

Where independence enters. Let P = (3000, 0.90), Q = (6000, 0.45), R = 0 and α = 2/900. Then αP + (1−α)R = (3000, 0.002) and αQ + (1−α)R = (6000, 0.001). Independence says the first pair and this mixed pair must have the same order. The data reverse it.

The condition on π. Allow weights: π(0.90)u(3000) > π(0.45)u(6000) and π(0.001)u(6000) > π(0.002)u(3000). Dividing, π(0.45)/π(0.90) < u(3000)/u(6000) < π(0.001)/π(0.002). This is subproportionality: shrinking every probability by the same factor does not shrink the weights by that factor. In particular, the low-probability pair (0.002, 0.001) is weighted much more aggressively than the high-probability pair (0.90, 0.45).

Note. The contradiction is independent of the curvature of u. That is why it is evidence about the probability weights, not about risk aversion.

Lecture 5

Reference-Dependent Preferences

Source: lecture 5 Reference Dependent.pptx — 42 slides Cabdrivers → Kőszegi–Rabin → effort experiment Three 《世说新语》 cases

Lecture 4 gave value a reference point and left the reference point exogenous. This lecture asks where it comes from and what happens when it is a belief about the future. The opening evidence is a field puzzle: New York taxi drivers appear to work fewer hours on high-wage days, the opposite of intertemporal substitution. The explanation the lecture develops is a daily income target — narrow bracketing plus a reference point at the target.

The second half is the formal model of Kőszegi and Rabin (2006). Utility is consumption plus a gain–loss term measured against the expectation, not the status quo. Under certainty this changes little; under uncertainty the reference point is itself a distribution, and gains and losses arise even when the realised outcome matches the plan. The model's sharp prediction — bunching at the fixed payment — is then tested in a real-effort experiment.

The deck is mostly equations on image-led slides. Every formula and every number below was read off the rendered slide. Two places where the slide's algebra is loose are flagged in place rather than silently corrected: the shopping example in §6 and the definition of the personal equilibrium in §7.

Concept map

from a field anomaly to an equilibrium concept

The puzzleTaxi drivers quit earlier on high-wage days.

what the standard model predicts

Intertemporal substitutionWork more when the wage is high, rest when it is low.

Observed elasticityNegative, and smaller for inexperienced drivers.

Narrow bracketingDecide one day at a time, not over the month.

the candidate explanation

Target incomePast income, expectations, social comparison.

Daily targetStop once the day's earnings reach the target.

Reference dependenceUtility is measured from the target, not from zero.

the formal model (Kőszegi–Rabin 2006)

CertaintyU(c, r) = m(c) + μ[m(c) − m(r)].

Uncertain outcomeIntegrate the gain–loss term over outcomes.

Uncertain referenceIntegrate over both outcome and reference distributions.

Multiple dimensionsAdditive separability across goods.

equilibrium and test

Personal equilibriumThe plan is optimal given the expectation of making it.

Preferred PESelect the PE with the highest ex-ante utility.

Effort experimentHigh fixed payment raises effort; bunching at the payment.

The cabdriver puzzle

slides 2–6

The lecture opens with a field setting in which the standard labour-supply prediction is easy to state and hard to reconcile with the data. A New York City cabdriver's trip sheet records, for each trip, the pickup and drop-off times and the fare. Fares are set by the Taxi and Limousine Commission, so the driver faces a daily wage that varies with demand — conventions, weather, the time of day — rather than a wage the driver chooses.

Field Which way does the labour supply curve slope?

The question: when the transitory wage is high, should the driver work more? The neoclassical answer is yes — intertemporal substitution: work while the wage is high and consume leisure when it is low, across days.

The observed wage elasticity of labour supply is negative: on high-wage days drivers stop earlier, not later.
The negative elasticity is smaller for inexperienced drivers than for experienced ones.
The pattern is hard to square with a driver who smooths consumption over a month and treats each day's wage as a price.

The lecture's reading: drivers make the decision one day at a time — narrow bracketing — and set a loose daily income target, quitting once they reach it.

The slides state the two empirical regularities without a numerical estimate. The workbench therefore does not attach one. The original field study is Camerer, Babcock, Loewenstein and Thaler (1997), “Labor Supply of New York City Cabdrivers: One Day at a Time”, QJE; the deck's slides 2–6 follow its framing.

Why the targets are reference points. A target can be anchored in three places the slide names: past income or consumption, an expectation for the future, and social comparison. Each turns the day's earnings into a gain or a loss relative to a benchmark rather than a quantity to be smoothed. If the marginal utility of a gain above the target is low and the marginal disutility of falling short is high, the driver stops near the target even when the wage is unusually high.

? What would falsify the story?

The target story is not simply “drivers are lazy on good days”. It predicts that the stopping rule responds to the target, not only to the wage: a driver with a higher daily target should work longer at the same wage, and a driver whose target is met early should stop earlier. The slide's closing instruction — “ask the taxi drivers on their decision criteria next time” — is a reminder that the mechanism is inferred, not directly observed in the trip sheets.

Reference points in the wild

slides 7–10

Two non-market examples make the same point before the model arrives: a reference point can be a round number, and it can be a person.

Marathon Round numbers and bunching

Distribution of marathon finishing times, n = 9,789,093. The dark bars highlight the density in the one-minute bin just before each 30-minute threshold. Allen, Dechow, Pope and Wu (2016), Figure 2.

Finishing times bunch just below 3:00, 3:30, 4:00, 4:30 and so on.
The same physical distance is run, but a time of 3:59:40 is a different outcome from 4:00:10.
The threshold is a goal: runners accelerate to avoid missing it, so the density jumps before the round number.

A round number is a reference point that costs nothing to announce and changes behaviour. This is the cleanest large-sample evidence in the lecture that goals are real.

Lady Hsieh and Master Wang 《世说新语 · 贤媛》 26

王凝之谢夫人既往王氏，大薄凝之。既还谢家，意大不说。太傅慰释之曰：“王郎，逸少之子，人材亦不恶，汝何以恨乃尔？”答曰：“一门叔父，则有阿大、中郎。群从兄弟，则有封、胡、遏、末。不意天壤之中，乃有王郎！”

Hsieh Tao-yun, having married into the Wang family, held her husband Wang Ning-chih in contempt. When she returned home unhappy, her uncle Hsieh An tried to console her: Wang Ning-chih was, after all, the son of Wang Hsi-chih and not a bad man in his own right. Her answer named her uncles and cousins one by one — all of them distinguished — and ended: “I never imagined that between heaven and earth there could be someone called Master Wang.”

The slide's reading is a social-comparison reference point. Wang Ning-chih was not evaluated in isolation; he was evaluated against the men of the Hsieh household. The same man can be a good match or a disappointment depending on the benchmark. This is the third source of targets in §2, stated as a story rather than a regression.

Gu Kaizhi and the sugarcane 《世说新语 · 排调》 59

顾长康啖甘蔗，先食尾。问所以，云：“渐至佳境。”

Gu Kaizhi always began a sugarcane at the tip, the least sweet part, and worked towards the middle. Asked why, he said: “By slow degrees I enter the realm of delight.”

The slide places this beside the marathon and the income target as a case of sequencing and anticipation. The value of each bite depends on where it sits in the sequence, not only on how much sugar it contains — the same structural point as a reference point that moves with the plan.

The Kőszegi–Rabin model: the certainty case

slides 11–14

The model replaces the status quo with the expectation. If a person expects a painful dental procedure and the procedure turns out to be unnecessary, the relief is a gain; if the procedure happens as expected, there is no gain and no loss. The reference point is therefore not where you are but what you expected.

Classical model: U(c, r) = m(c)

Kőszegi–Rabin: U(c, r) = m(c) + μ[ m(c) − m(r) ]

There are two components: standard monetary utility m(c), and gain–loss utility μ[m(c) − m(r)]. The function μ is increasing, μ(0) = 0, and it is kinked at zero — losses hurt more than equal-sized gains please. The deck's linear simplification writes consumption itself as the argument:

U(c, r) = c + η(c − r) if c ≥ r; U(c, r) = c + λη(c − r) if c < r.

Here η is the weight on gain–loss utility and λ > 1 is loss aversion. The slide uses μ in the general form and η in the linear form; the workbench keeps both names and treats them as the same weight.

Job A lower-paid job with a lower reference point

Evaluate a job offer against your previous job. Situation 1: the previous job paid 300/day; the offer pays 300/day. Situation 2: the previous job paid 400/day; the offer pays 350/day.

Situation 1: U(300, 300) = 300 + η(300 − 300) = 300.
Situation 2: U(350, 400) = 350 + ηλ(350 − 400) = 350 − 50ηλ.
If ηλ > 1, then 300 > 350 − 50ηλ.

The lower-paid job with the lower reference point can be preferred. The extra 50 in money does not compensate for the 50 shortfall against a higher expectation.

! The kink is doing the work

At λ = 1 and η > 0, Situation 2 is 350 − 50η, which is still below 300 whenever η > 1 — but the model is then symmetric and the reference-point effect is weaker. Loss aversion, λ > 1, is what makes the shortfall loom large enough to overturn a higher absolute wage for a plausible η.

Uncertainty in the outcome and in the reference point

slides 15–21

Expected utility replaces u(cᵢ) by the expectation Σ pᵢ m(cᵢ). Kőszegi–Rabin replaces u(cᵢ) by u(cᵢ, r) and integrates the gain–loss term over the outcome distribution.

U(c, r) = Σᵢ pᵢ [ m(cᵢ) + μ( m(cᵢ) − m(r) ) ]

Two jobs Uncertain outcome, certain reference point

Situation 1: the previous job paid 300/day. The offer pays 300 with probability 0.5 and 200 with probability 0.5.
Situation 2: the previous job paid 400/day. The offer pays 350 with probability 0.5 and 250 with probability 0.5.

Situation 1: U = 0.5[300 + η(0)] + 0.5[200 + ηλ(200 − 300)] = 250 − 50ηλ.
Situation 2: U = 0.5[350 + ηλ(350 − 400)] + 0.5[250 + ηλ(250 − 400)] = 300 − 100ηλ.
Situation 1 is preferred again exactly when ηλ > 1.

Adding outcome risk does not remove the reference-point effect; it adds a second loss state.

Uncertainty in both. When the reference point is itself a lottery (q_j, r_j), the agent evaluates each outcome against each possible reference point, weighting the pair by the product of the probabilities:

U(c, r) = Σᵢ Σⱼ pᵢ qⱼ [ m(cᵢ) + μ( m(cᵢ) − m(rⱼ) ) ]

The slide's worked case is a previous job paying 300 or 250 with probability 0.5 each, and a new job paying 300 or 200 with probability 0.5 each. There are four outcome–reference pairs, each with probability 0.25:

Outcome \ Reference	q₁ = 0.5, r = 300	q₂ = 0.5, r = 250
p₁ = 0.5, c = 300	300 + η(300 − 300)	300 + η(300 − 250)
p₂ = 0.5, c = 200	200 + ηλ(200 − 300)	200 + ηλ(200 − 250)

U = 0.25[300 + η(0)] + 0.25[200 + ηλ(−100)] + 0.25[300 + η(50)] + 0.25[200 + ηλ(−50)] = 250 + 12.5η − 37.5ηλ

The slide also writes the same expression grouped by outcome, with the reference point replaced by its mean 300q + 250(1 − q). At q = 0.5 the mean is 275, and the two forms agree: 0.5[300 + 25η] + 0.5[200 − 75ηλ] = 250 + 12.5η − 37.5ηλ. The grouped form is the one to remember: the reference point enters as a distribution, and the agent feels a gain or a loss in every state where the outcome differs from a possible reference.

Multiple dimensions and the shopping problem

slides 22–25

Consumption has many dimensions. The model assumes utility is additively separable across them, with a gain–loss term for each:

U(c, r) = Σₖ mₖ(cₖ) + Σₖ μ[ mₖ(cₖ) − mₖ(rₖ) ]

Shoes Buying in Xinjiekou

You are in Xinjiekou (新街口) looking at a pair of shoes with price p. Your reservation value is 1. Assume p is deterministic. Consumption has two dimensions, m(c) = c₁ + c₂, where c₁ ∈ {0, 1} is whether you have the shoes and c₂ is wealth. Normalise wealth to 0, so c₂ is minus the price paid. Utility is linear.

Classical theory: buy when p ≤ 1.
If you expect to buy, the reference is (shoes 1, payment −p). Buying gives 1 − p; not buying gives −ηλ + ηp. Buying is better when p ≤ (1 + ηλ)/(1 + η) ≡ p_H. Since λ > 1, p_H > 1: easier to buy.
If you do not expect to buy, the reference is (0, 0). Buying gives 1 − p + η − ηλp; not buying gives 0. Buying is better when p ≤ (1 + η)/(1 + ηλ) ≡ p_L. Since λ > 1, p_L < 1: harder to buy.

The same price can be acceptable or unacceptable depending on what you expected to do. On [p_L, p_H], expectations are self-fulfilling: expect to buy → buy; expect not to buy → not buy.

! A slip in the slide's algebra

Slide 25's middle line writes the payment term under “do not expect to buy” as η(0 − (−p)). The slide's own table on slide 24 gives that cell as ηλ((−p) − 0) = −ηλp, and the final inequality p ≤ (1 + η)/(1 + ηλ) requires the minus term. The line in the prose is missing the λ and has the sign reversed. The workbench uses the table's form; the threshold on the slide is correct.

Model 11

When is “I'll buy it” self-fulfilling?

Set the price, the weight on gain–loss utility and loss aversion. The bar shows the three regions: below p_L only “buy” is a personal equilibrium, above p_H only “not buy” is, and in between both are. The preferred personal equilibrium is still the neoclassical one — buy below the reservation value, not buy above it.

Personal equilibrium and preferred personal equilibrium

slides 26–28

So far the purchase expectation has been exogenous. Kőszegi and Rabin (2006) make it endogenous with an equilibrium concept. People have time to plan before they act; the plan can still be revised; and the planned choice itself is the reference point. Rational expectations require two things: the actual choice coincides with the planned choice, and the plan is optimal given the expectation of making it.

Definition. Given a choice set ℒ, a lottery L ∈ ℒ is a personal equilibrium (PE) if U(L | L) ≥ U(L′ | L) for all L′ ∈ ℒ.

Read the notation carefully: U(L | L) means the utility of choosing L when L is also the reference point. A PE is a plan that, if you expect it, you have no incentive to abandon.

In the shopping example with deterministic plans only, {Buy, Not Buy}:

Buy is a PE ⇔ 1 − p ≥ −ηλ + ηp ⇔ p ≤ p_H = (1 + ηλ)/(1 + η)

Not Buy is a PE ⇔ 0 ≥ (1 − p) + η − ηλp ⇔ p ≥ p_L = (1 + η)/(1 + ηλ)

Because λ > 1, p_L < 1 < p_H. The price line therefore has three regions: below p_L, Buy is the unique PE; between p_L and p_H, both Buy and Not Buy are PE; above p_H, Not Buy is the unique PE.

Selection. When there are multiple equilibria, the agent chooses the one with the highest ex-ante utility. A PE L is a preferred personal equilibrium (PPE) if, for any other PE L′, U(L | L) ≥ U(L′ | L′). In the shopping example, U(Buy | Buy) = 1 − p and U(Not Buy | Not Buy) = 0, so the PPE is Buy if p ≤ 1 and Not Buy if p > 1.

? Why the model needs uncertainty to depart from the benchmark

Under certainty, the realised outcome equals the expectation, the gain–loss terms vanish, and ex-ante utility reduces to m(c). PE already yields multiple, self-fulfilling equilibria — but PPE does not depart from the neoclassical prediction. The departure requires an uncertain reference point, for example a random price: then the reference is a distribution, and gains and losses arise even when the outcome matches the plan. That is the bridge from §5 to the effort experiment.

Effort provision: the theoretical prediction

slides 29–38

The experiment tests the expectation-based reference point in a labour market. Subjects count zeros in tables of 150 randomly ordered zeros and ones. In stage 1 they work for four minutes at a piece rate of 10 cents per correct answer, for sure. In stage 2 they choose how long to work, up to 60 minutes. One of two cards in an envelope determines the pay: with probability 0.5 a piece rate of 20 cents per correct answer, and with probability 0.5 a fixed payment — 3 euros in the LO treatment, 7 euros in the HI treatment. The subject chooses the stopping time before drawing the card.

The standard model. Let w be the piece rate, e effort (correct answers), and f the fixed payment. With separable utility in income and effort:

U(x, e) = u(x) − c(e) = f/2 + we/2 − c(e)

∂U/∂e = w/2 − c′(e) = 0 ⇒ c′(e*) = w/2

The fixed payment drops out. Effort is independent of f, so LO and HI should produce the same average effort.

A status-quo reference point does not help. If the reference point is the status quo on entering the experiment, it is the same in both treatments. Effort can change how piece-rate earnings compare with the status quo, but it cannot change the potential loss relative to the status quo if the fixed payment is realised. Varying f therefore has no impact on effort incentives even with reference-dependent preferences.

The expectation-based reference point. The agent expects either we or f, each with probability 0.5. There are four outcome–reference cells, each with probability 0.25. If the intended stopping point is below the fixed payment (we < f):

U = we/2 + f/2 − c(e) + ¼η(f − we) + ¼ηλ(we − f)

If the stopping point is above it (we ≥ f):

U = we/2 + f/2 − c(e) + ¼η(we − f) + ¼ηλ(f − we)

Differentiate each branch:

we < f: c′(e) = w/2 + (w/4)η(λ − 1)

we ≥ f: c′(e) = w/2 − (w/4)η(λ − 1)

Below the fixed payment, the marginal return to effort is higher than w/2: working more reduces the chance of a painful shortfall. Above it, the marginal return is lower: working more gives up the fixed payment's protection and creates a possible loss. The result is a downward jump in marginal benefit at e = f/w, and effort bunches at that kink.

Raising f moves the kink to the right and keeps the high marginal return in force up to a higher effort level. The prediction is therefore:

Average effort in the HI treatment is higher than in the LO treatment. The mechanism is not that people like the fixed payment; it is that a larger fixed payment makes the reference point larger, so the region in which effort protects against a loss is longer.

Model 12

Bunching at the fixed payment

Marginal benefit is a step: high below f/w, low above it. The upward-sloping line is marginal cost. When the two branches would cross on opposite sides of the kink, the optimum is the kink itself — the bunching prediction. Raise the fixed payment and the high-benefit region lengthens.

? What the lab adds, and what it does not

The slide's illustration uses a generic convex cost function and plots marginal benefit against effort for f = 3 and f = 7. The lab makes the same figure numerical with c(e) = e²/400 and a piece rate of 20 cents, so that the kink and the optimum can be read off. The quadratic cost is the lab's choice, not the paper's; the bunching result holds for any increasing marginal cost that crosses the step.

Effort provision: results and alternatives

slides 39–42

Results LO against HI

Average accumulated earnings at which subjects stopped working.

Treatment	Mean stopping earnings	Modal choice
LO · fixed payment 3 euros	7.37 euros	3 euros
HI · fixed payment 7 euros	9.22 euros	7 euros

Average effort is higher in HI: 9.22 against 7.37 euros of accumulated earnings.
The modal stopping point is exactly the fixed payment in each treatment: 3 in LO, 7 in HI. That is the bunching prediction.
The standard model and the status-quo reference model both predict no treatment effect.

The data match the expectation-based model on both margins: the mean shifts up, and the mode sits on the fixed payment.

Alternative explanations. The lecture considers two, and both were tested with additional treatments:

Explanation	Test	What would happen if it were the whole story
Salience	NOSAL: the two cards read “5 euros plus acquired earnings” and “8 euros”, so the fixed payment is folded into the show-up fee. In LO the cards read “Acquired earnings” and “3 euros”. The show-up fee is 5 euros in both treatments.	If salience were the mechanism, expressing the fixed payment as part of the show-up fee should reduce or remove the treatment difference.
Reciprocity	R: identical to LO except an additional lump sum of 4 euros is announced at the start of the main stage.	If reciprocity were the mechanism, the extra gift should raise effort. Effort in R and LO is not different.

The slide reports that effort in R and LO is not different, which rules out the simple gift-exchange story. The NOSAL design removes the difference in how the fixed payment is described, which addresses salience.

§ The lecture's closing summary

Preferences are reference dependent. The open questions are which reference points people use, how they form, how they move, and where the model applies — labour markets, finance, housing, and settings not yet studied. The cabdriver, marathon and effort results are three answers; they are not a general theory of where the reference point comes from.

What the lecture establishes

four claims, and their evidence

1 · The reference point can be an expectation

The dental-procedure example and the job comparison. Utility is m(c) plus a gain–loss term against what was expected, not against the status quo.

2 · Targets in the field

Negative wage elasticity among cabdrivers; round-number bunching at marathon thresholds. Both are consistent with a daily target, though neither identifies it uniquely.

3 · PE is a coherence requirement

A plan must be optimal given the expectation of making it. Multiple PE are possible; PPE selects the best one. Under certainty PPE equals the neoclassical choice.

4 · The model has a sharp test

A higher fixed payment lengthens the region where effort protects against a loss. Average effort rises, and the mode sits on the fixed payment: 7.37 → 9.22 euros, modes 3 and 7.

Summary sheet

printable

Kőszegi–Rabin utility

U(c, r) = m(c) + μ[m(c) − m(r)]

Two components: standard utility and gain–loss utility relative to the reference point r.

Linear form

c + η(c − r) if c ≥ r; c + λη(c − r) if c < r

η is the weight on gain–loss utility; λ > 1 is loss aversion.

Uncertain outcome, certain reference

U = Σᵢ pᵢ [m(cᵢ) + μ(m(cᵢ) − m(r))]

The job example: Situation 1 = 250 − 50ηλ; Situation 2 = 300 − 100ηλ.

Uncertain in both

U = Σᵢ Σⱼ pᵢ qⱼ [m(cᵢ) + μ(m(cᵢ) − m(rⱼ))]

Four cells at 0.25 each in the lecture's example: 250 + 12.5η − 37.5ηλ.

Multiple dimensions

U = Σₖ mₖ(cₖ) + Σₖ μ[mₖ(cₖ) − mₖ(rₖ)]

Additive separability across goods; shopping is the two-dimension case.

Shopping thresholds

p_L = (1 + η)/(1 + ηλ) < 1 < p_H = (1 + ηλ)/(1 + η)

Below p_L, Buy is the unique PE; between, both; above p_H, Not Buy is unique. PPE: Buy iff p ≤ 1.

Personal equilibrium

U(L | L) ≥ U(L′ | L) for all L′ ∈ ℒ

The plan is optimal given the expectation of making it.

Preferred personal equilibrium

U(L | L) ≥ U(L′ | L′) for every other PE L′

Selection by ex-ante utility when several PE exist.

Standard effort

U = f/2 + we/2 − c(e); c′(e*) = w/2

The fixed payment drops out: no treatment effect.

Reference-dependent effort

we < f: c′(e) = w/2 + (w/4)η(λ−1); we ≥ f: c′(e) = w/2 − (w/4)η(λ−1)

A downward jump at e = f/w; effort bunches there. Higher f extends the high-benefit region.

Headline results

LO mean 7.37 euros, mode 3; HI mean 9.22 euros, mode 7. Marathon n = 9,789,093 with bunching below 30-minute thresholds.

Alternatives ruled out

Reciprocity: effort in R and LO does not differ. Salience: NOSAL equalises the card descriptions. The treatment effect survives the second design.

Key concepts

English term · 中文

Term	中文	Meaning in this lecture
Reference-dependent preferences	参照点依赖偏好	Utility depends on outcomes relative to a reference point, not only on levels.
Reference point	参照点	Past income, an expectation, or a social comparison — the benchmark for gains and losses.
Narrow bracketing	窄框定	Deciding one day at a time rather than smoothing over the month.
Target income	目标收入	A loose daily earnings target at which the driver stops.
Intertemporal substitution	跨期替代	The standard prediction: work more when the wage is temporarily high.
Bunching	聚集	Excess mass just below a threshold or at a kink.
Gain–loss utility	得失效用	μ[m(c) − m(r)]: the second component of the Kőszegi–Rabin utility.
Loss aversion	损失厌恶	λ > 1: a loss of a given size hurts more than a gain of the same size pleases.
Personal equilibrium (PE)	个人均衡	A plan that is optimal given the expectation of making it.
Preferred personal equilibrium (PPE)	最优个人均衡	The PE with the highest ex-ante utility when several exist.
Self-fulfilling expectation	自我实现的预期	Expect to buy → buy; expect not to buy → not buy, on [p_L, p_H].
Status-quo reference point	现状参照点	Using the entry state as the benchmark; predicts no treatment effect in the effort experiment.
Expectation-based reference point	基于预期的参照点	Using the distribution of expected outcomes as the benchmark; predicts bunching at f.
Salience	显著性	An alternative explanation: the fixed payment draws attention; tested with NOSAL.
Reciprocity	互惠	An alternative explanation: a gift raises effort; tested with the R treatment.

Self-check

graded, with explanations

0 / 0 correct

The field puzzle and the model

Q1Why is a negative wage elasticity of labour supply among cabdrivers puzzling for the standard model?

Correct.The standard model treats a high transitory wage as a high price for leisure and predicts substitution toward work. The negative elasticity is the anomaly the lecture explains with narrow bracketing and a daily income target.

Not quite.Drivers do choose when to stop, and the fare schedule is the source of wage variation. The puzzle is the direction of the response: high-wage days produce fewer hours, not more.

Q2Which set is the slide's list of sources for a reference point?

Correct.Slide 5 names exactly these three. The Kőszegi–Rabin model formalises the second; the Lady Hsieh case illustrates the third.

Not quite.The lecture's list is past income or consumption, expectations for the future, and social comparison. The status quo is one candidate, not the definition.

Q3In U(c, r) = m(c) + μ[m(c) − m(r)], what is the second term?

Correct.m(c) is standard monetary utility; the second term evaluates the same outcome against the reference point. μ is increasing, μ(0) = 0, and it is kinked at zero.

Not quite.The term is the gain–loss component. It vanishes when c = r, is positive above r, and negative below r — with the negative side steeper when λ > 1.

Q4With ηλ > 1, which job does the certainty-case comparison prefer?

Correct.U(300,300) = 300, while U(350,400) = 350 − 50ηλ. When ηλ > 1 the second is below 300, so the lower-paid, lower-reference job wins.

Not quite.Compare the utilities, not the wages. The 350 job carries a 50 shortfall against a 400 reference, and with ηλ > 1 that shortfall costs more than 50.

Personal equilibrium

Q5In the shopping example, what happens to the buying threshold when the buyer expects to buy?

Correct.If buying is the reference point, not buying is a loss on both dimensions. The buyer is willing to pay a premium above the reservation value to avoid that loss, so p_H > 1.

Not quite.The expected buyer treats not buying as the deviation, and a deviation is a loss. That makes buying acceptable at a higher price, not a lower one.

Q6What defines a personal equilibrium?

Correct.The reference point in the comparison is the plan itself. A PE is self-enforcing: expecting it gives no reason to revise it.

Not quite.Feasibility is not enough, and the status quo is not the reference point. The definition compares the plan against every alternative using the plan as the reference.

Q7Why does the preferred personal equilibrium coincide with the neoclassical prediction under certainty?

Correct.Under a deterministic plan the reference equals the outcome, so μ(0) = 0 in every state. Multiple PE can still exist because each plan is self-fulfilling, but selecting the best one brings you back to the classical ranking.

Not quite.λ is still greater than 1; it simply has nothing to act on when there is no gap between outcome and reference. The departure requires uncertainty in the reference point.

Effort provision

Q8Why does a higher fixed payment increase average effort in the Kőszegi–Rabin model?

Correct.Below f/w the marginal return is w/2 + (w/4)η(λ−1); above it, w/2 − (w/4)η(λ−1). Raising f moves the kink right and extends the high-return region, which raises average effort and produces bunching at f.

Not quite.The piece rate is 20 cents in both treatments, and reciprocity is ruled out by the R treatment. The mechanism is the higher reference point and the longer high-marginal-benefit region.

Q9Derive the two shopping thresholds and show why the price region between them contains two personal equilibria. Then explain the slip in slide 25.

Set-up. Two dimensions: shoes c₁ ∈ {0,1} and payment c₂ = −p if you buy, 0 if not. Reservation value 1, linear utility, so the classical payoff is 1 − p for Buy and 0 for Not Buy.

Expect to buy. Reference (1, −p). Buy: 1 − p, no gain or loss. Not Buy: 0 − 1 = −1 on shoes, a loss of ηλ; and 0 − (−p) = +p on payment, a gain of ηp. So Not Buy is −ηλ + ηp. Buy is at least as good iff 1 − p ≥ −ηλ + ηp, i.e. p ≤ (1 + ηλ)/(1 + η) = p_H.

Expect not to buy. Reference (0, 0). Buy: 1 − p plus a gain of η on shoes and a loss of ηλp on payment, so 1 − p + η − ηλp. Not Buy: 0. Buy is at least as good iff 1 + η ≥ p(1 + ηλ), i.e. p ≤ (1 + η)/(1 + ηλ) = p_L.

Two equilibria. For p between p_L and p_H, Buy is optimal when Buy is expected, and Not Buy is optimal when Not Buy is expected. Both are personal equilibria; the expectation is self-fulfilling. Below p_L only Buy is a PE; above p_H only Not Buy is.

The slip. Slide 25 writes the payment term under “do not expect to buy” as η(0 − (−p)) = +ηp. The table on slide 24 gives ηλ((−p) − 0) = −ηλp, and the slide's own threshold (1 + η)/(1 + ηλ) requires the loss term. The prose line is missing λ and has the sign reversed; the table and the threshold are correct.

Q10Derive the two first-order conditions for effort and explain the bunching prediction in your own words.

Four cells. The outcome is we with probability 0.5 and f with probability 0.5; the reference point is also we or f with probability 0.5. Each of the four cells has probability 0.25.

Below the fixed payment (we < f). When the outcome is we and the reference is we, the gain is 0. When the outcome is f and the reference is we, the gain is f − we. When the outcome is we and the reference is f, the loss is we − f, weighted by λ. When both are f, the gain is 0. Summing the four quarter-weighted terms gives ¼η(f − we) + ¼ηλ(we − f).

Differentiating we/2 + f/2 − c(e) plus that term: w/2 − c′(e) − ¼ηw + ¼ηλw = 0, hence c′(e) = w/2 + (w/4)η(λ − 1).

Above the fixed payment (we ≥ f). The gain–loss term is ¼η(we − f) + ¼ηλ(f − we). Differentiating gives c′(e) = w/2 − (w/4)η(λ − 1).

Bunching. Marginal benefit jumps down at e = f/w. If the high-branch optimum lies above the kink and the low-branch optimum lies below it, neither branch is feasible: utility rises up to the kink and falls after it, so the optimum is exactly the kink. A mass of subjects stops at accumulated earnings equal to the fixed payment — which is what the modes 3 and 7 show.

Why higher f raises effort. The kink moves right, so the high-marginal-benefit branch covers more effort levels. The average stopping point rises, as the 7.37 → 9.22 comparison shows.

Lecture 6

Gender

Source: lecture 6 gender.pptx — 48 slides Seven factors → the tournament experiment → culture Four 《世说新语》 cases

This lecture is an application, not a new model. It takes the behavioural toolkit — reference points, beliefs, risk, competition — and asks how much of the gender wage gap it can explain. The organising device is a list of seven factors: participation, education, experience and hours, motherhood, occupation and firm, discrimination, and norms and psychological attributes. The first six are mostly labour economics; the seventh is where the behavioural evidence enters.

The centrepiece is Niederle and Vesterlund (2007): men enter tournaments much more often than women even when performance is identical. Four explanations are separated — taste for competition, overconfidence, risk aversion and feedback aversion — and the paper's own decomposition attributes about 57% of the gap to the general factors and 43% to the residual “competitive” component. The lecture then asks whether competition is biology or culture, using the Khasi and Maasai comparison.

Most of the lecture's charts are images; the numbers below were read off the rendered slides. Where a slide gives a citation but not a figure, the workbench says so rather than filling the gap.

Concept map

seven factors, three mechanisms, one experiment

The factWomen earn less than men, on average, in every country with data.

what the gap is made of

1 · ParticipationWho is in the labour force, and selection.

2 · EducationThe gap closed, then reversed.

3 · Experience & hoursInterruptions and the price of temporal flexibility.

4 · MotherhoodThe child penalty, causal and selected.

where the gap is located

5 · Occupation, industry, firmThe largest single factor; together with industry, over half.

6 · DiscriminationTaste, statistical discrimination, implicit bias.

7 · Norms and psychologyNegotiation, risk, competition, non-cognitive skills.

the behavioural test

Tournament entryNiederle & Vesterlund (2007): 35% of women, 73% of men.

Four explanationsTaste · overconfidence · risk · feedback aversion.

Decomposition57% general, 43% residual competition.

CultureKhasi and Maasai reverse the pattern.

The gap, and the 2023 Nobel

slides 3–4

Claudia Goldin won the 2023 Nobel Prize in Economics “for having advanced our understanding of women's labour market outcomes”. The citation credits her with the first comprehensive account of women's earnings and labour-market participation through the centuries, and with identifying both the causes of change and the main sources of the remaining gap. This lecture follows that structure: first the long-run facts, then the factors that produce them.

Trend The US female-to-male earnings ratio

Female-to-male earnings ratios of full-time workers, 1955–2014. Blau and Kahn (2017), “The Gender Wage Gap: Extent, Trends, and Explanations”, Journal of Economic Literature, Figure 1.

The ratio is flat or falling from the late 1950s to about 1980, at roughly 60%.
It rises steeply through the 1980s and 1990s, then more slowly after 2000.
By the end of the series the weekly series is near 83% and the annual full-year series near 78%. The gap between the two lines is itself informative: women work fewer hours and fewer weeks than men, so the annual gap is larger than the weekly one.

The headline is not a constant gap. It is a falling gap with a remaining gap, and the remaining gap is what the seven factors are meant to explain.

The ratios are read off the chart. The notes on the slide specify workers aged sixteen and over from 1979 onward, and fourteen and over before 1979 — the series is not composition-constant across the whole period.

? What a raw ratio does and does not measure

A female-to-male earnings ratio among full-time workers controls for full-time status but not for occupation, experience, hours within full-time work, or selection into employment. Every factor in the rest of the lecture is a candidate explanation for the part that remains. The ratio is a fact to be decomposed, not a measure of discrimination.

Factor 1: labour-force participation

slides 5–9

Who is in the labour force determines whose wages are observed. The slide names five forces behind the rise in women's participation: rising wages, increasing educational attainment, improvements in household technology (Greenwood, Seshadri and Yorukoglu, 2005), the birth control pill (Goldin and Katz, 2002), and shifts in preferences (Cotter, Hermsen and Vanneman, 2011; Fortin, 2015).

Chart Participation rates, 1947–2014

Female and male labour-force participation rates, age sixteen and over. Blau and Kahn (2017), Figure 3; Current Population Survey.

Male participation declines from about 86% in 1947 to about 69% in 2014.
Female participation rises from about 32% to about 57% over the same period.
The two series converge but do not meet; the remaining participation gap is part of why the observed wage gap is not the same as the gap among all potential workers.

Selection matters. The slide names the wage offers versus observed wages distinction and the Heckman two-step estimator: if the women who work are not a random sample of women, observed wages do not estimate the wage offer distribution.

The U-curve. Female participation is not monotonically increasing over history. Industrialisation made it harder for many married women to combine work with family because work moved out of the home; Goldin documented this using data from more than ten thousand female household heads in eighteenth-century Philadelphia. Even though many unmarried women were employed in manufacturing — in some states up to 40% of all young women worked in industry — total female labour-force participation declined. Participation then rose again in the twentieth century: the U in the long-run series.

2017 Participation around the world

Female labour-force participation rate, 2017.

Region	Rate
China	61%
North America	56%
European Union	51%
World	49%
India	<30%
Arab world	21%

The slide's photograph is the 1950s–60s poster slogan 妇女能顶半边天 — “women hold up half the sky”. The chart is the quantitative version of the slogan, and China's 61% is the highest rate listed.

? “Changing expectations”

The slide for this idea is a line drawing: a woman with children, a man with children, and a young woman walking toward a signpost whose two arrows read EXPECTATIONS and OPPORTUNITIES. The point is not a regression result. It is that girls' expectations about future work — formed before they choose education — can shift ahead of the opportunities actually available, and that the shift feeds back into participation.

Factor 2: education

slides 10–11

Reversal From minority to majority

Share of degrees earned by women in the United States.

Degree	1971	2011
Bachelor's	43%*	57%
Associate	—	62%
Master's	—	61%
PhD	14%	51%
Post-college professional	6%	49%

By 1980, women had caught up with men in college graduation.
By 2011 they earned a majority of bachelor's, associate and master's degrees, and about half of PhDs and professional degrees.
The education gap has not merely narrowed; at several levels it has reversed.

The slide gives 1971 and 2011 values. The 1971 figure of 43% is for bachelor's and associate degrees combined, not for each separately, so the associate cell is left blank; the master's 1971 figure is likewise not on the slide. The table does not split a combined number.

Why the gap narrowed. The slide lists six channels: human-capital investment became more attractive because women's expected working lives lengthened and participation rose; occupational segregation fell; Title VII of the Civil Rights Act applied to government jobs; familial attitudes and social gender norms changed; Title IX constrained discrimination by educational institutions; and the pill lowered the cost of investing in a career.

Why women now surpass men. Three mechanisms are offered:

Assortative mating

Family-related income gains from marrying a high-earning partner are larger for women than for men, so the family return to college rose more for women.

Non-cognitive skills

Girls have lower non-pecuniary costs of college, fewer behavioural problems, more homework, lower ADHD diagnosis rates and earlier maturation — so they respond more to the same rise in the benefit of college.

Math gap closed

Boys no longer have a higher average maths score in high school, removing a previously relevant comparative advantage.

Factor 3: labour-force experience and work hours

slides 12–13

Women's working lives are shorter and more discontinuous, largely because of family responsibilities. Three consequences follow:

Less on-the-job training. Women have lower incentives to invest in training, especially firm-specific training, because the expected period over which the return can be collected is shorter.
A wage penalty for temporal flexibility. Some occupations reward long, continuous, predictable hours. Lawyers are Goldin's (2014) example; the slide also points to Bertrand, Goldin and Katz (2010) on the salaries of MBAs from Chicago, 1990–2006.
Selection into occupations with different hours profiles. The penalty is not only about total hours but about when the hours are worked and how substitutable one worker is for another.

? The slide's figure is a picture of the mechanism

The “wage penalty for temporal flexibility” slide is a line drawing, not a regression: people walking along two parallel paths, one at a higher earnings level, and a parent with a child dropping onto the lower path. The visual is the argument — a career interruption or a demand for flexible hours moves a worker onto a lower earnings trajectory — and the slide cites the MBA evidence rather than plotting it.

Factor 4: motherhood

slides 14–16

The motherhood wage penalty is the negative relationship between children and women's wages. The lecture separates two ways it can arise:

Causal channels

Women may quit the labour market to give birth; firms may therefore invest less in firm-specific training; motherhood may reduce productivity at work; and employers may discriminate.

Selection

Women who have children may differ systematically from those who do not in ways that also affect wages, so the raw correlation is not the causal effect.

Evidence Two experiments, two answers

The slide cites two pieces of evidence in opposite directions.

Correll, Benard and Paik (2007): a laboratory study of résumé evaluations plus a field experiment. Motherhood is penalised relative to otherwise identical childless women.
Williams and Ceci (2015): in academic labour markets, they find no motherhood penalty.

The penalty is not universal across labour markets. The two results are the lecture's warning against treating “the motherhood penalty” as one number.

China 申超 (2020), 《社会》

Chinese Household Nutrition Survey (CHNS), 1989–2015. The estimated coefficient on motherhood in a wage equation, by year and model.

The baseline coefficient is about −0.10 in 1989 and about −0.20 in 2015: the penalty roughly doubles over the period.
Adding controls for family structure, education and job characteristics moves the coefficient up, but the downward trend remains. In the full model the 2015 coefficient is about −0.14.
The slide's conclusion is that the motherhood wage penalty becomes more severe over time in China.

The coefficients are read off the plotted lines in the slide's Figure 5. The chart's four series are the baseline model, +family structure, +education, and +job characteristics. A second chart (Figure 12) splits the sample by sector: the penalty is roughly flat near −0.10 in the state sector and falls from about −0.10 to about −0.18 in the non-state sector.

! Read the sign, not just the trend

A coefficient of −0.20 is a log-wage difference of about 20 log points, which is roughly an 18% lower wage, not a 20% lower wage. The slide reports coefficients; the workbench keeps the coefficient scale and does not relabel it as a percentage of earnings.

Factor 5: occupations, industries and firms

slides 17–18

In 1970 women were concentrated in administrative support, service occupations, teaching and nursing; men in managerial jobs, blue-collar occupations, law, medicine and engineering. Segregation has declined since 1970, but the slide's key quantitative claim is structural: occupation is still the largest single factor accounting for the gender wage gap, with industry second; taken together they account for over one-half of the gap.

Within occupations, there is a second gap at the top. Women are relatively new arrivals in many senior roles, and it takes time to move up through the ranks. The slide names the glass ceiling, discrimination, and a higher probability that women quit the occupation (Gayle, Golan and Miller, 2012). The CEO and professor examples are the same mechanism at different rungs: representation falls as the rank rises, and the fall is not fully explained by the pipeline alone.

? Composition versus the same job

“Occupation and industry account for over half” is a statement about the composition of employment. It does not say that within the same occupation and industry women are paid the same. A decomposition can assign a large share to occupation while a within-occupation gap remains, because the two questions are different. Keep the level of aggregation in view.

Factor 6: discrimination

slides 19–20

Becker Discrimination as a taste

Becker (1951): discrimination is a taste, and it produces a wage differential between men and women.

Employers who dislike employing women will hire them only at a wage discount large enough to compensate for the disutility.
Male workers who dislike working with women will demand a wage premium, raising men's relative wages.
Customers who are reluctant to buy from women make women less productive in revenue terms, depressing their relative wages.
Competition should erode employer discrimination in the long run: the least discriminatory firms hire cheaper female labour, have lower costs, and drive the others out. Discrimination therefore survives in sectors that are not competitive.

The prediction is sharp: in a competitive market, employer taste discrimination cannot persist. That is why the evidence on the remaining gap points to sources other than a simple employer taste.

Phelps Statistical discrimination

Phelps (1972): groups may differ in the expected value of productivity or in the reliability with which productivity can be predicted.

If employers use group membership as a signal, they may pay women less, exclude them from jobs requiring substantial firm-specific training, or deny them promotions.
The mechanism does not require anyone to dislike women. It requires only that the group average is used to predict the individual.
This is the bridge from a taste model to a belief model — the subject of Lecture 3.

Implicit discrimination (Bertrand, Chugh and Mullainathan, 2005) adds a third channel, measured with the Implicit Association Test: an automatic association can operate without the person endorsing it.

Factor 7: norms, psychological attributes and non-cognitive skills

slides 21–25

The slide's premise is that a sizeable component of any outcome is not explained by traditional economic variables, and that experimental economics has supplied a body of candidate mechanisms. It also gives the standard warning: laboratory results need external validity.

Negotiation

Women are much less likely to negotiate salaries, raises or promotions (Babcock and Laschever, 2003). The lecture gives two reasons and one moderator:

Backlash. A woman who negotiates can trigger a negative response from others, so the expected return to negotiating is lower.
Negotiating for others. Gender differences in negotiating outcomes are reduced when the negotiator acts on behalf of another person.
Institutional clarity. Leibbrandt and List (2015) run a field experiment: whether the vacancy explicitly states that wages are negotiable matters for who negotiates.

Risk aversion

Croson and Gneezy (2009) survey laboratory experiments and find that women are, on average, more risk averse than men. Two limits are stated on the slide: the difference is not found among mutual-fund managers (which could be selection or learning), and risk aversion does not explain within-occupation earnings differences.

Competitiveness

This is the mechanism the lecture pursues. The slide opens with three 《世说新语》 cases in which competition is visible in behaviour rather than inferred from a survey.

A debate that became a duel 《世说新语 · 文学》

孙安国往殷中军许共论，往反精苦，客主无闲。左右进食，冷而复暖者数四。彼我奋掷麈尾，悉脱落，满餐饭中。宾主遂至莫忘食。殷乃语孙曰：“卿莫作强口马，我当穿卿鼻。”孙曰：“卿不见决鼻牛，人当穿卿颊。”

Sun Anguo went to debate with Yin Hao. The argument went back and forth without pause; the food brought by attendants went cold and was warmed again four times. Both men waved their horsetail whisks so hard that the hairs fell into the meal, and host and guest forgot to eat until evening. Yin finally said: “Don't act the strong-mouthed horse — I'll pierce your nose.” Sun replied: “Haven't you seen a nose-split ox? Someone will pierce your cheek.”

The slide uses the story for competition as a disposition: the debate is not only about arriving at the truth, it is a contest that both men are trying to win. The whisk-throwing is the behavioural tell. This is the same distinction the tournament experiment makes between ability and preference for performing under competition.

Shi Chong and Wang Kai 《世说新语 · 汰侈》

石崇与王恺争豪，并穷绮丽，以饰舆服。……崇曰：“不足恨，今还卿。”乃命左右悉取珊瑚树，有三尺四尺，条干绝世，光彩溢目者六七枚，如恺许比甚众。恺惘然自失。

Shi Chong and Wang Kai competed in extravagance, each exhausting the finest materials on carriages and clothes. When the emperor gave Wang Kai a coral tree about two feet tall, Wang showed it to Shi Chong, who smashed it with an iron ruyi. Wang was furious; Shi said it was not worth regretting, and had his attendants bring out six or seven coral trees three and four feet tall, far finer than Wang's. Wang was left dazed and diminished.

The second case is competition over rank, not money: the point of the display is to establish a hierarchy. The slide pairs it with the debate because both show that the act of competing can carry utility independent of the prize. That is Explanation 1 in the tournament experiment.

Xie Daoyun and the willow catkins 《世说新语 · 言语》

谢太傅寒雪日内集，与儿女讲论文义。俄而雪骤，公欣然曰：“白雪纷纷何所似？”兄子胡儿曰：“撒盐空中差可拟。”兄女曰：“未若柳絮因风起。”公大笑乐。

On a snowy day Xie An gathered the family to discuss literature. When the snow suddenly thickened he asked what it resembled. His nephew said: “It is like salt scattered in the air.” His niece Xie Daoyun said: “Not as good as willow catkins rising on the wind.” Xie An laughed with pleasure.

The slide places this under “gender difference in ability”, and the placement is deliberately provocative: the best answer in the room comes from the girl. The story is not evidence that women and men differ in ability; it is a reminder that judgments of ability are made inside a social setting, and that the benchmark against which a performance is judged is part of the outcome. The lecture uses it to set up the question of whether the tournament gap is about ability at all — the experiment's answer is that measured performance is the same.

Do women shy away from competition?

slides 26–40

Niederle and Vesterlund (2007, QJE) ask whether women are less likely to compete, and whether that can explain the gender gap in top management and politics. The headline result is that men enter the tournament more than women. The experiment is designed to separate four explanations:

1 · Taste for competition

Men enter because they like to compete, independent of the money.

2 · Overconfidence

Men enter because they overestimate their relative performance.

3 · Risk aversion

Men enter because they are less averse to the risk of earning nothing.

4 · Feedback aversion

Men enter because they are less averse to learning how they rank.

Design Four tasks, one randomly paid

A real-effort task: adding sets of two-digit numbers, five minutes, no calculator but scratch paper allowed, computerised with z-Tree. Participants know whether each answer is correct. Forty men and forty women, in groups of four.

Task 1 — piece rate. 50 cents per correct answer.
Task 2 — tournament. The highest scorer in the group receives $2 per correct answer; the others receive nothing.
Task 3 — choose the scheme for future performance. Before a five-minute task, participants choose piece rate or tournament. The tournament benchmark is the Task-2 tournament performance of the other group members.
Task 4 — choose the scheme for past piece-rate performance. Participants choose whether their Task-1 performance is paid at 50 cents per answer or as a tournament. This is an individual decision: it affects no one else's earnings and does not depend on others' entry.
Belief elicitation. Guess your rank in Task 1 and Task 2; $1 per correct guess. Risk attitude measured with a Holt–Laury lottery.

Task 3 is the key: entry depends on your ability to beat others' Task-2 performance and on your preference for competing, but not on your beliefs about whether others will enter Task 3. That closes a channel: if men believed women would not enter, they would face fewer competitors and the odds would change.

Model 13

Piece rate or tournament?

The experiment's Task 3 in one decision. A tournament pays $2 per correct answer only if you beat the others; a piece rate pays 50 cents regardless. Set your expected score, your subjective chance of winning, and any non-pecuniary value of competing. The break-even win probability is where the two expected payments meet.

Results The 35–73 gap

Task 3: share choosing the tournament.

Group	Share entering the tournament
Women	35%
Men	73%

Performance does not differ between men and women in either the piece rate or the tournament. The CDFs of correctly solved problems nearly coincide.
The entry gap survives conditioning on performance: performance does not matter much, and only gender remains significant.
Beliefs do matter: entry rises with guessed rank. But at every guessed rank the male line is above the female line.
Overconfidence: both sexes are overconfident relative to actual rank, but men more so — 75% of men think they are best in their group of four, against 43% of women.
Decomposition: about 57% of the original gender effect is accounted for by general differences in overconfidence, risk aversion and feedback aversion. The residual “competitive” component is 43%.

The gap is not a performance gap. It is a decision gap, and more than half of it is explained by general psychological differences rather than by a taste for competition alone.

? Extensions and limits

The design has no between-group control and treatment groups; the comparison is within the experiment. The slide lists extensions: different tasks (verbal versus maths), different incentives (money versus a book voucher for one's children), culture, changing the gender composition of the group, and using lab performance to predict field choices. Buser, Niederle and Oosterbeek (2014) measured competitiveness in Dutch high-school classrooms and followed students' education choices: boys were substantially more likely to choose the more prestigious profile, and about 23% of that difference could be explained by competitiveness.

Culture and gender

slides 41–46

If competitiveness is a stable trait, the gap should look the same everywhere. Gneezy, Leonard and List (2009, Econometrica) compare two societies with opposite gender systems: the Maasai of Kenya, a patriarchal society, and the Khasi of India, a matrilineal society.

Design Tossing a tennis ball into a bucket

In a four-sided house, one group sits on side 1 and another on side 2; they are led one by one to sides 3 and 4 and do not know the identity of the other group. Each session has one male and one female experimenter. The task: toss a tennis ball into a bucket three metres away, ten chances. Participants choose the payment scheme before performing.

Option 1: X per successful shot, regardless of the other participant's performance.
Option 2: 3X per successful shot if they outperform the randomly matched other participant, and nothing otherwise.

The choice is a clean measure of willingness to compete: the only difference between the options is the tournament element.

Results The pattern reverses

Share choosing the competitive option.

Society	Women	Men
Maasai · patriarchal	0.26	0.50
Khasi · matrilineal	0.54	0.39

In the patriarchal society, women are less competitive than men: 0.26 against 0.50.
In the matrilineal society, the result reverses: women 0.54, men 0.39.
Khasi women are even slightly more competitive than Maasai men (0.54 against 0.50).

The gender difference in competitiveness is not invariant across societies. Whatever produces it, it is at least partly cultural.

The numbers are read off the slide's table and bar chart. The regression table with controls shows the Female coefficient is negative in the pooled and Maasai samples and positive in the Khasi sample; the Khasi × female interaction is positive and significant in the pooled specification.

Is it risk? A parallel risk-aversion experiment (Gneezy and Potters) gives subjects an endowment of 100 units and asks what portion to bet in a lottery that returns three times the bet with probability one-half and nothing with probability one-half. The slide reports no gender differences in risk attitudes in this setting, which weakens the risk explanation for the cultural reversal.

Nature versus nurture. The slide's discussion is deliberately open. Gender is not only a biological phenomenon. Alesina, Giuliano and Nunn (2013) connect the historical use of the plough in agriculture to gender inequality today; the slide asks whether China's textile-industry development, the price of tea, or orchard agriculture can play the same role. It ends with a question rather than a verdict: does the Khasi–Maasai comparison provide causal evidence between culture and competitiveness?

! What the comparison can and cannot establish

Two societies differ in many things besides kinship. A reversal is strong evidence against the claim that the gender gap in competitiveness is universal, but it is not by itself a causal estimate of “culture”. The slide's own closing question is the right one to keep in view.

What works, and a closing case

slides 47–48

The lecture's penultimate slide is the cover of Iris Bohnet's What Works: Gender Equality by Design. The title is the argument: rather than trying to change people's preferences, change the design of the institutions in which they choose — the structure of evaluation, the default, the way a job is advertised. This connects the gender lecture back to the default effects of Lecture 2 and the framing effects of Lecture 1.

“I have long been on terms with myself” 《世说新语 · 品藻》

桓公少与殷侯齐名，常有竞心。桓问殷：“卿何如我？”殷云：“我与我周旋久，宁作我。”

Huan Wen and Yin Hao were equally famous in their youth, and Huan was always competitive. Huan asked Yin: “How do you compare with me?” Yin replied: “I have been on terms with myself for a long time; I would rather be myself.”

The lecture closes on this exchange after a term of competition experiments. The 《世说新语校释》 reading quoted on the slide is that no one knows a person as well as that person knows himself, and no one loves him as much: “I have been on terms with myself for a long time.” Yin's answer may contain self-promotion, but it also refuses the ranking. The connection to the lecture is the distinction between competing and being measured by the competition — the same distinction that separates a taste for competition from a belief about one's rank.

Summary sheet

printable

The headline trend

US female-to-male earnings ratio: roughly 60% around 1980, about 83% weekly and 78% annual by 2014 (Blau & Kahn, 2017).

Participation

US women 32% → 57%, men 86% → 69%, 1947–2014. Long-run U-curve: industrialisation moved work out of the home.

Global participation, 2017

China 61% · North America 56% · EU 51% · world 49% · India <30% · Arab world 21%.

Education

1971 → 2011: bachelor's 43% → 57%; PhD 14% → 51%; professional 6% → 49%. Women overtook men in college graduation by 1980.

Experience and hours

Interruptions reduce firm-specific training; temporal flexibility carries a wage penalty (lawyers; Chicago MBAs 1990–2006).

Motherhood

Correll et al. (2007) find a penalty; Williams & Ceci (2015) do not in academic markets. China (申超 2020, CHNS 1989–2015): coefficient ≈ −0.10 → −0.20, penalty worsens.

Occupation and industry

Occupation is the largest single factor; industry is second; together they account for over half of the gap.

Discrimination

Becker's taste model predicts competition erodes employer discrimination; Phelps's statistical discrimination does not require taste; implicit discrimination is measured with the IAT.

Tournament entry

Task 3: 35% of women and 73% of men choose the tournament; performance does not differ; 75% of men and 43% of women believe they are best in their group.

Decomposition

About 57% of the gender effect is accounted for by overconfidence, risk aversion and feedback aversion; the residual competitive component is 43%.

Culture

Maasai: women 0.26, men 0.50. Khasi: women 0.54, men 0.39. The pattern reverses; a parallel risk experiment finds no gender difference.

What works

Iris Bohnet: change institutional design rather than preferences. The closing 《世说新语》 case refuses the ranking: 「我与我周旋久，宁作我」.

Key concepts

English term · 中文

Term	中文	Meaning in this lecture
Gender wage gap	性别工资差距	The difference between women's and men's earnings, raw or adjusted.
Female-to-male earnings ratio	女性与男性收入比	The reciprocal measure; about 60% around 1980 and about 80% by 2014 in the US.
Labour-force participation	劳动参与率	The share of the population working or seeking work.
Selection	选择偏差	Observed wages are not wage offers when employment is not random.
Heckman two-step estimator	Heckman 两步法	A correction for selection into the observed sample.
U-curve	U 形曲线	Female participation falls with industrialisation, then rises.
Human capital	人力资本	Training and education whose return depends on the expected working life.
Firm-specific training	企业专用培训	Training valuable at one firm; less attractive when the expected tenure is shorter.
Temporal flexibility penalty	时间灵活性惩罚	A wage cost of needing flexible or discontinuous hours.
Motherhood wage penalty	母职工资惩罚	The negative association between children and women's wages.
Occupational segregation	职业隔离	The concentration of men and women in different occupations.
Glass ceiling	玻璃天花板	A barrier to advancement at higher ranks that is not explained by the pipeline alone.
Taste discrimination	偏好型歧视	Becker: a distaste for employing or working with a group.
Statistical discrimination	统计性歧视	Using group averages to predict an individual's productivity.
Implicit discrimination	内隐歧视	Automatic associations measured by the Implicit Association Test.
Tournament	锦标赛	A pay scheme that rewards relative rather than absolute performance.
Overconfidence	过度自信	Believing one's rank is better than it is.
Feedback aversion	反馈厌恶	Aversion to learning how one ranks relative to others.
Matrilineal / patriarchal	母系 / 父系	The kinship systems compared in the Khasi–Maasai study.
Nature versus nurture	先天与后天	Whether a gender difference is biological, cultural, or both.

Self-check

graded, with explanations

0 / 0 correct

The seven factors

Q1What does the female-to-male earnings ratio in the opening chart measure?

Correct.The chart plots female-to-male earnings ratios of full-time workers. It controls for full-time status but not for occupation, experience or hours within full-time work, so the remaining gap still needs the seven-factor decomposition.

Not quite.Participation is a different series. The earnings ratio compares the wages of women and men who are working full time; it is the object the lecture decomposes.

Q2Why is female labour-force participation a U-curve over the long run rather than a monotonic rise?

Correct.Goldin's account: manufacturing work left the household, so the home-based combination of work and family became harder. Unmarried women worked in industry — up to 40% of young women in some states — but total female participation declined before the twentieth-century rise.

Not quite.The mechanism is the location of work, not a cycle in preferences or a fall in wages. Industrialisation separated the workplace from the household.

Q3Which statement about the education gap is supported by the slide's numbers?

Correct.The slide's 1971/2011 pair is 14% → 51% for PhDs and 6% → 49% for post-college professional degrees. Women also moved from 43% to 57% of bachelor's degrees and from 43% to 62% of associate degrees.

Not quite.The reversal is broad, not confined to one degree. Check the 1971 column: 43% bachelor's, 14% PhD, 6% professional.

Q4What is the temporal flexibility penalty?

Correct.Lawyers and the Chicago MBA sample are the slide's examples. The penalty is about the structure of hours, not just their number, and it is one reason an interruption lowers the earnings trajectory.

Not quite.It is not a formal tax or a vacation effect. It is the market price of flexibility in occupations where one worker is not a close substitute for another at short notice.

Q5Why does the lecture insist on distinguishing causal channels from selection in the motherhood penalty?

Correct.Correll et al. (2007) find a penalty and Williams and Ceci (2015) do not in academic markets. Both the selection issue and the cross-market variation argue against treating a single correlation as a universal causal parameter.

Not quite.The issue is what the comparison identifies. If mothers differ from non-mothers in unobserved productivity or job attachment, the observed gap mixes the effect of children with those differences.

Q6According to the slide, how much of the gender wage gap do occupation and industry together account for?

Correct.Occupation is the largest single factor, industry second, and together they account for more than half. That is a statement about composition, not about equal pay within the same occupation.

Not quite.The slide's claim is over one-half, split between occupation (largest) and industry (second).

Discrimination and competition

Q7What does Becker's taste model predict about employer discrimination in a competitive market?

Correct.Discriminatory employers forgo cheaper female labour, so their costs are higher. Competition should drive them out, which is why the taste model locates persistent discrimination in non-competitive sectors.

Not quite.A taste is a cost to the employer, not a profit source. Firms that indulge it pay more for labour than firms that do not.

Q8How does statistical discrimination differ from Becker's taste discrimination?

Correct.Phelps (1972). The employer uses group membership as a signal. The mechanism can persist without anyone preferring not to employ women, and it is the bridge to the belief-and-overconfidence material.

Not quite.Statistical discrimination is a belief mechanism, not a taste. The employer is trying to predict productivity and uses the group average as an input.

Q9What are the headline Task-3 entry rates in Niederle and Vesterlund (2007)?

Correct.Task 3: 35% of women and 73% of men choose the tournament. Performance does not differ between the sexes in Task 1 or Task 2.

Not quite.The direction is women lower, men higher: 35% against 73%. The 25/50 pair is not the headline result.

Q10How does the paper decompose the entry gap?

Correct.The general psychological factors explain a majority — about 57% — leaving 43% as the residual “competitive” component. The paper's point is that most of the gap is not a pure taste for competition.

Not quite.The 57/43 split is between general factors (overconfidence, risk, feedback aversion) and the residual competition component. It is not a split between overconfidence and risk.

Q11What does the Khasi–Maasai comparison show?

Correct.Maasai women 0.26 against men 0.50; Khasi women 0.54 against men 0.39. The reversal argues that the gap is at least partly cultural. It does not by itself prove a causal effect of culture.

Not quite.The point of the study is the reversal. One society shows the usual direction, the other shows the opposite.

Q12Why is Task 3 in Niederle and Vesterlund (2007) designed as it is? Explain what the design rules out.

The choice. In Task 3, before performing a five-minute addition task, a participant chooses between a piece rate (50 cents per correct answer) and a tournament ($2 per correct answer if her score beats the other group members' Task-2 tournament scores).

Why the Task-2 benchmark. The performance of a participant who enters the tournament is compared with the performance of people who actually performed under tournament incentives in Task 2. This avoids comparing a tournament entrant with people who chose a piece rate and might have exerted different effort.

What it rules out. Entry depends only on the person's own ability to beat the others' past tournament performance and on her preference for competing. It does not depend on her beliefs about whether other participants will enter Task 3. If men believed women would not enter, a simultaneous competition would give men better odds — only one competitor instead of three. Task 3 breaks that channel.

What Task 4 adds. Task 4 applies the same choice to past piece-rate performance. It is an individual decision that affects no one else and does not depend on others' entry, so it isolates the general factors — overconfidence, risk aversion, feedback aversion — from the specific act of competing. If those factors alone caused the gap, the gap should appear in Task 4 as well.

The result. The gap is 35% against 73% in Task 3. Performance is the same. About 57% of the gap is accounted for by the general factors; 43% remains as the competitive component.

Q13Does the Khasi–Maasai study establish that culture causes the gender difference in competitiveness? Defend your answer.

What the study shows. Two societies with opposite kinship systems produce opposite gender gaps: Maasai women 0.26 against men 0.50; Khasi women 0.54 against men 0.39. The Khasi result reverses the usual sign, and Khasi women are slightly more competitive than Maasai men. A parallel risk experiment finds no gender difference in risk attitudes, weakening one alternative explanation.

What it does not show. The two societies differ in many dimensions besides kinship: income, the organisation of production, the gender composition of the experimenters' interactions, and the meaning of the task. Without random assignment to culture, the comparison is not a causal estimate of “culture” as a single treatment.

The defensible conclusion. The study is strong evidence against the hypothesis that the gender gap in competitiveness is a fixed, universal trait. It is consistent with a cultural explanation and it motivates the history-based work (Alesina, Giuliano and Nunn on the plough; China's textile and tea history). The slide's own closing question — “Do you think this experiment provides causal evidence between culture and competitiveness?” — is the right level of caution.

Roadmap

What is still to come

From the topic slide of Lecture 1 Weeks 5–16 are placeholders Updated as the decks arrive

Six lectures have been delivered. The course's own topic slide sets out fourteen subjects across three parts, and this page tracks which of them the workbench can currently say anything about. The remaining lectures will be built into this page as they are posted — the same five blocks per lecture, with a model where a model is what the material needs.

Lecture by lecture

the instructor's own sequencing

Lecture 1

Introduction

The two-question experiment
What behavioral economics is, and the three pillars
History of ideas · the four currents
Lab, field, field data, structural estimation

Built · 2 models

Lecture 2

Choice under Certainty

Preference-based and choice-based approaches
The weak axiom and Sen's Property α
Six departures from rational choice

Built · 4 models

Lecture 3

Belief

Two systems and attribute substitution
Representativeness, availability, anchoring
Overconfidence and belief elicitation
Prediction markets and motivated beliefs

Built · 2 models

Lecture 4

Risk

St Petersburg, expected utility and the axioms
Reference dependence and the value function
Probability weighting and the Allais paradox
Cumulative prospect theory, 1992

Built · 2 models

Lecture 5

Reference-Dependent Preferences

Cabdrivers, target income and narrow bracketing
Kőszegi–Rabin: expectations as reference points
Personal equilibrium and preferred personal equilibrium
Effort provision, bunching and the 7.37 / 9.22 result

Built · 2 models

Lecture 6

Gender

Seven factors behind the wage gap
Niederle & Vesterlund: 35% against 73% tournament entry
Overconfidence, risk and the 57/43 decomposition
Khasi and Maasai: culture and competitiveness

Built · 1 model

Lecture 7 +

Time

Exponential versus quasi-hyperbolic discounting
Present bias and commitment devices
Time inconsistency in the field

Waiting for the deck

Later

Others, Games, Culture

Social preferences and inequality aversion
Level-k and quantal response equilibrium
Applications: culture, policy design

Waiting for the deck

Adding a lecture. The build is componentised: a lecture lives in one file under _build/parts/, and python build.py reassembles the single-file workbench and its installable shell from scratch. The pipeline, the three verification scripts and the three known traps are documented in _build/README.md.

《世说新语》 index

every story used in the six lectures, and what it illustrates

The stories are not decoration. Each one is placed in the lecture next to the concept it illustrates, and the mapping from story to model is the point — several of them illustrate a concept more memorably than the experiment does. The six lectures use twenty-four of them. Collected here so the whole device can be seen at once.

Read them the way the lecture does: as illustrations of mechanisms that the experiments establish. A story that can be read as a bias is not evidence of one.

Story	Section of 《世说新语》	Illustrates	Lecture
王戎 and the roadside plums 道边苦李	雅量	Rational inference in a child — and the puzzle of preference change in the same person	L1 §5
王戎 drilling the plum pits 钻核售李	俭啬	The other half of that puzzle: the same man, a different preference ordering	L1 §5
王戎 refusing the condolence money	德行	The counter-evidence: generous in mourning, miserly in trade	L1 §5
The Xinting gathering 新亭对泣	言语	The Nanjing setting of the lectures themselves	L1 §5
阮宣子's “将无同” 三语掾	文学	A failure of completeness — a relation that declines to rank	L2 §2
Zu Shao and Ruan Yaoji 祖士少好财，阮遥集好屐	雅量	The choice-based approach: 「于是胜负始分」 — ranking revealed by behaviour	L2 §4
Wang Ziyou turning back 乘兴而行，兴尽而返	任诞	Sunk cost correctly ignored	L2 §9
朝三暮四	《庄子 · 齐物论》	Framing effect: 「名实未亏而喜怒为用」	L2 §10
Wang Dun at the lavatory 王敦如厕	纰漏	Status quo bias: old habits carried into a new setting	L2 §12
Sun Zijing's slip 漱石枕流	排调	Slips versus biases: noise, and the rationalisation that follows it	L2 §13
Chang'an or the sun 长安何如日远	夙惠	Availability: distance inferred from how readily examples come to mind	L3 §2
Jing Fang and hindsight 将恐今之视古	规箴	Hindsight bias, and the curse of knowledge	L3 §9
Mars in the Supreme Tenuity 荧惑入太微	言语	Correlation treated as causation: an omen read from a sequence	L3 §12
Guo Pu and the dragon's ear 葬龙耳	术解	The social use of vague prophecy: it fits whatever happens	L3 §12
The plum grove 望梅止渴	假谲	Belief has real consequences even when false	L3 §12
Huan Wen at the gaming board 袁耽掷帽	任诞	Gambling as a measurement of risk attitude — and its limits	L4 §3
Xie Xuan's sachet 赌香囊	假谲	The same domain: risk taken inside a game, inference made outside it	L4 §3
Huan Wen and the conquest of Shu 观其蒲博	识鉴	The stability of risk attitude across domains — stated as an assumption	L4 §3
Lady Hsieh and Master Wang 不意天壤之中，乃有王郎	贤媛	A social-comparison reference point: the husband is judged against the men of her own family	L5 §3
Gu Kaizhi and the sugarcane 渐至佳境	排调	Sequencing and anticipation: the value of each bite depends on its place in the sequence	L5 §3
Sun Anguo and Yin Hao 奋掷麈尾	文学	Competition as a disposition: a debate pursued as a contest, not only as a search for truth	L6 §9
Shi Chong and Wang Kai 石崇与王恺争豪	汰侈	Competition over rank: the display is the point, independent of the prize	L6 §9
Xie Daoyun and the willow catkins 未若柳絮因风起	言语	Ability judged in a social setting: the best answer comes from the girl	L6 §9
Yin Hao and Huan Wen 我与我周旋久，宁作我	品藻	Refusing the ranking: competing is not the same as being measured by the competition	L6 §12

The departures at a glance

one table, with the source each one comes from

Departure	Canonical source	Headline result	Model
Isolation effect	Kahneman & Tversky (1979), Econometrica 47(2), Problems 11–12	Two identical problems answered inconsistently by a majority
Prospect theory	Tversky & Kahneman (1992), J. Risk & Uncertainty 5	α = 0.88, λ = 2.25, γ = 0.61 — the median estimates
Menu dependence	Huber, Payne & Puto (1982), JCR; Simonson (1989)	Beer 43% → 63%; batteries 43% → 60%
Endowment effect	Kahneman, Knetsch & Thaler (1990), JPE	Median WTA $5.25 against median WTP $2.75; 4/1/2/2 trades against 11 predicted
Sunk cost	Ho, Png & Reza (2016); Tiefenbeck et al. (2016)	High-sunk-cost cars are driven more, and their usage decays faster with age	—
Status quo bias	Johnson & Goldstein (2003), Science 302	Effective consent ranges from 4.25% to 99.98% across 11 European countries
Framing effect	Tversky & Kahneman (1981), Science 211	72/28 under one description, 22/78 under its equivalent	—
Default effects in the field	Allcott (2011); He, Pan, Park, Sawada & Tan (2023), Science 381	≈2% less household electricity; +648% “no cutlery” orders
Conjunction fallacy	Tversky & Kahneman (1983)	Most respondents rank “bank teller and feminist” above “bank teller”, violating P(A∧B) ≤ P(A)	—
Base-rate neglect	Eddy (1982); Gigerenzer & Hoffrage (1995)	1% prevalence, 90% sensitivity, 10% false positive → posterior ≈ 8.3%, not 90%
Anchoring	Tversky & Kahneman (1974)	Median UN estimate 25 after anchor 10, 45 after anchor 65; the wheel is visibly random	—
Overconfidence	Moore & Healy (2008); Alpert & Raiffa (1982)	About 50% of true values fall outside stated 90% intervals	—
Allais paradox / common ratio	Allais (1953); Tversky & Kahneman (1979), Problems 7–8	(3000, 0.90) ≻ (6000, 0.45) and (6000, 0.001) ≻ (3000, 0.002) require contradictory ratios
Reference dependence / loss aversion	Kahneman & Tversky (1979); Tversky & Kahneman (1992)	λ = 2.25, α = β = 0.88; B1 ≻ A1 and A2 ≻ B2 in the 1,000/2,000 experiment
Probability weighting	Kahneman & Tversky (1979); Tversky & Kahneman (1992)	π(0.66) + π(0.34) < 1; π(p) > p for small p; π(rp) > rπ(p)
Reference-dependent labour supply	Camerer, Babcock, Loewenstein & Thaler (1997); Allen, Dechow, Pope & Wu (2016)	Negative wage elasticity among cabdrivers; round-number bunching in 9,789,093 marathon times	—
Expectation as reference point	Kőszegi & Rabin (2006); Abeler, Falk, Goette & Huffman (2011)	LO 7.37 against HI 9.22 euros; modes 3 and 7 at the fixed payment
Tournament entry	Niederle & Vesterlund (2007), QJE	35% of women and 73% of men enter; 57% of the gap explained by general factors, 43% residual
Culture and competitiveness	Gneezy, Leonard & List (2009), Econometrica	Maasai women 0.26 against men 0.50; Khasi women 0.54 against men 0.39	—

? The entries with no model of their own

Sunk cost and framing are both, formally, reference-point phenomena — and both are already visible in the models that exist. The Asian disease result is the isolation effect of Model 1 with different words; the Singapore car result is a sunk cost behaving like the endowment effect's mirror image. The belief entries (conjunction, anchoring, overconfidence) are mechanisms rather than value functions: they are explained in Lecture 3 with the experiments that established them, and only base-rate neglect has a figure whose inputs can be moved. That is a choice about what a model adds, not a gap in the coverage.

Reading list

as given on the slide

Item	Author	What it is for
《行为新语》讲义	—	The course's own notes. The first thing to read.
Lecture Notes in Microeconomic Theory	Rubinstein	The choice-theory half of Lecture 2, at the same level. The lecture cites Chapters 1–3.
Experimetrics	Peter Moffatt	How to analyse experimental data — the statistics behind “t-test, nonparametric tests”.
Behavioral Game Theory	Colin Camerer	For the strategic half of the course: level-k, QRE, learning.
An Introduction to Behavioral Economics	David R. Just	A textbook, for reference rather than for reading through.
Misbehaving	Richard Thaler	The fullest narrative history of the field.
Thinking, Fast and Slow	Daniel Kahneman	The two-systems framework — the spine of the Beliefs lecture.
《世说新语》	刘义庆著，刘孝标注	A course reading in its own right, not a source of illustrations.

The slide also refers to a paper list. It has not been distributed yet; when it is, it belongs on this page rather than in the lectures.

The papers Lectures 3 and 4 cite by name

Item	Author	Where it is used
“Maps of bounded rationality”	Kahneman (2003), AER	The two-system framework and the definition of attribute substitution
“Judgment under uncertainty: heuristics and biases”	Tversky & Kahneman (1974), Science	The three heuristics; the anchoring wheel
“Extensional versus intuitive reasoning”	Tversky & Kahneman (1983), Psychological Review	The Linda problem and the conjunction fallacy
“Prospect theory: an analysis of decision under risk”	Kahneman & Tversky (1979), Econometrica	Editing and evaluation phases; the 1979 weighting function
“Advances in prospect theory: cumulative representation of uncertainty”	Tversky & Kahneman (1992), Journal of Risk and Uncertainty	CPT, the value-function estimates, and the numerical die example
“Subjective probability and the theory of games”	Hossain & Okui (2013), REStat	The binarized scoring rule
“The wisdom of crowds”	Galton (1907), Nature	The ox at the Plymouth fair
“Prediction markets”	Wolfers & Zitzewitz (2004), JEP	Contract design and the market's aggregate probability

✎ The one book to actually finish

The slide's own instruction: none of Thinking, Fast and Slow, Misbehaving or The Undoing Project is a textbook, and you should try to finish at least one this semester. They do different jobs: Kahneman for the content, Thaler for how the field happened, Lewis for why the two central collaborators stopped working together.

What you will get from this course

slide 44

Main theories

Prospect theory · quasi-hyperbolic discounting · inequity aversion · the level-k model. Four theories; the workbench carries prospect theory twice, once as the 1979 value-and-weighting model and once as the 1992 cumulative model on a six-outcome gamble.

New skills for an economist

Run lab and field experiments. Think about many things using new perspectives. Think critically about the research literature — replication crisis, causality.

Begin your own research

A research project, which is the reason the methods material in Lecture 1 comes as early as it does.

Assessment

Classroom performance 20% · two problem sets 20% · final exam 60%. The problem sets are the part where the weak axiom, the six departures, the Bayes calculations and the common-ratio algebra are most likely to be examined.

! Why the replication crisis is on this slide and not in an appendix

The course teaches experiments as the method, and then tells you to be sceptical of them. That is not a contradiction. An experiment is a procedure for making a claim refutable — and the replication crisis is what happens when the procedure is followed but the claim is still not robust: small samples, many outcomes measured, the analysis chosen after the data. Every experiment on the slides carries its N, and the workbench quotes them, for exactly this reason.

The same standard applies here. Where the slides give a number, the workbench reproduces it with its source; where they do not — the results of Johnson & Goldstein's online study, the treatment definitions behind the classroom double auction — it says so rather than filling the gap.