Behavioral Economics Workbench
A working study companion for Behavioral Economics (行为经济学), built from the two lecture decks supplied so far — Lecture 1 · Introduction and Lecture 2 · Choice under Certainty — 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.
How this workbench is organised
the same five blocks in every lectureHow 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.
Explanatory prose around the slides, with the lecture's own experiments taken apart and the technical definitions stated exactly as the deck states them.
Six 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.
The definitions, formulas and headline numbers of the lecture on one screen, in the order the lecture introduced them.
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.
Both 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.
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.
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 six figures.
The six models
each one attached to the lecture that needs itThe 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.
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.
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.
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.
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.
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.
What the course covers
from the topic slide of Lecture 1The course splits into three parts. Individual decision making is where Lectures 1 and 2 sit: what a rational choice is, and the six documented ways actual choices depart from it. 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.
Individual decision making
- Rationality · what the standard model assumes
- Beliefs · heuristics, biases, overconfidence
- Risk · prospect theory, reference points
- Time · present bias, discounting
Strategic decision making
- Others · social preferences, inequality aversion
- Games · level-k, quantal response equilibrium
- Experimental markets and learning
Application
- Gender
- Culture
- Nudging and policy design
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 |
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
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Introduction
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 buildsThe experiment the lecture opens with
slides 2–5The 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.
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.
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.
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.
- 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%
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 6–8The 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.
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.
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.
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 9The slide puts that sentence in quotation marks and then spends three points qualifying it. The qualifications are the examinable content.
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 11–14Before 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.
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。
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。
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.
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.
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.
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?”
History of ideas
slides 15–17I · For a long time, economics and psychology were one subject
The Theory of Moral Sentiments
on utility
on “impatience”
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. |
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 18–29I · Bounded rationality — Simon
“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.
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.
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). | — |
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.
- 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.
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.
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 32–40Four 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
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 |
- 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.
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.
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
printableKey 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 explanationsThe opening experiment
Definition and benchmark
History and the four currents
Methods
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.
Choice under Certainty
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 buildsThe preference-based approach
slides 3–6The 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.
The preference relation ≽ is rational if it possesses the following two properties:
“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。
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.
- 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
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 7Remark — 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.
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 8–10The second route refuses to talk about mental attitudes at all. It starts from what people are observed to pick.
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。
The choice structure (2B, C()) satisfies the weak axiom (WA) of revealed preference if the following property holds:
If for some A ∈ 2B with x, y ∈ A we have x ∈ C(A), then for any B ∈ 2B 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.
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 10In 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 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 ∅ ∉ 2B when it defines the choice structure.
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 11Proof: easy — see MWG p. 12
that is, if ≽ generates the choice structure (2B, C()).
then there is a rational preference relation ≽ that rationalises C() relative to 2B — that is, C(B) = C*(B, ≽) for all B ∈ 2B. Furthermore, this rational preference relation is the only preference relation that does so.
Proof: not required
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 lectureThe 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(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.
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.
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 $40” and “no show”.
Sunk cost 沉没成本
slides 14–16In scenario (A) above, people's buying decision is influenced by the lost ticket. The lecture's statement of the standard: a sunk cost should not be considered in rational decision making — don't cry over spilled milk.
王子猷居山阴,夜大雪,眠觉,开室,命酌酒。四望皎然,因起仿偟,咏左思招隐诗。忽忆戴安道,时戴在剡,即便夜乘小船就之。经宿方至,造门不前而返。人问其故,王曰:“吾本乘兴而行,兴尽而返,何必见戴?”
- High-sunk-cost cars drive more.
- Driving time decreases with the car's age.
- The decrease between driving time and car age is larger for the high-sunk-cost cars.
The figure on the slide plots average monthly usage by car age for three registration years, with average sunk costs of 16,921, 15,301 and 13,261 Singapore dollars, for the most popular model in the sample (3,403 cars). Usage starts high — around 2,700 km a month at five months — and flattens near 1,500 km by the mid-80s. The ordering of the three lines follows the ordering of the sunk costs for most of the range, which is the regression's raw material. The vertical axis is in kilometres and the sunk costs are in Singapore dollars — the figure's own note reads “average sunk cost S$”, 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。
| 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.
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- 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
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.
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.
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 24–28Status 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.
| 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.
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。
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.
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.
Summary sheet
printableProposition 3: WA + every subset of up to three elements ⟹ a rational ≽ rationalises C(), and it is the only one that does.
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 (2B, 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 explanationsThe two approaches
The departures
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 ∅ ∉ 2B when it defines 2B.
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.
What is still to come
Two 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 sequencingIntroduction
- The two-question experiment
- What behavioral economics is, and the three pillars
- History of ideas · the four currents
- Lab, field, field data, structural estimation
Choice under Certainty
- Preference-based and choice-based approaches
- The weak axiom and Sen's Property α
- Six departures from rational choice
Risk
- Expected utility and the independence axiom
- Prospect theory in full: value and weighting
- The Allais paradox, and probability weighting
Time
- Exponential versus quasi-hyperbolic discounting
- Present bias and commitment devices
- Time inconsistency in the field
Beliefs
- Heuristics: representativeness, availability, anchoring
- The two-systems framework
- Overconfidence, and motivated beliefs
Others, Games, Gender, Culture
- Social preferences and inequality aversion
- Level-k and quantal response equilibrium
- Applications: gender, culture, policy design
《世说新语》 index
every story used in the two lectures, and what it illustratesThe 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. 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 |
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 |
Sunk cost and framing are both, formally, reference-point phenomena — and both are already visible in the two models that do 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. That is why the lecture introduces prospect theory once and then reuses it.
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 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 44Prospect theory · quasi-hyperbolic discounting · inequity aversion · the level-k model. Four models, and this workbench now carries two of them interactively.
Run lab and field experiments. Think about many things using new perspectives. Think critically about the research literature — replication crisis, causality.
A research project, which is the reason the methods material in Lecture 1 comes as early as it does.
Classroom performance 20% · two problem sets 20% · final exam 60%. The problem sets are the part where the weak axiom and the six departures are most likely to be examined.
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.