““Constructed” preferencesConstructed” preferencesSS200 Colin CamererSS200 Colin Camerer

Preferences: “complete, transitive” u(x), tradeoffs among Preferences: “complete, transitive” u(x), tradeoffs among goodsgoods Historical note: Axioms not empirically well-founded. They Historical note: Axioms not empirically well-founded. They

were designed to provide simple mathematical framework for were designed to provide simple mathematical framework for aggregation (utilityaggregation (utility demand) and because Pareto won the demand) and because Pareto won the “what is utility?” battle“what is utility?” battle

““Constructed” suggests expression of preference is like Constructed” suggests expression of preference is like problem-solving: problem-solving: Will you vote for John Kerry? Will you vote for John Kerry? Answered by rapid intuition (tall, good hair) and/or deliberate Answered by rapid intuition (tall, good hair) and/or deliberate

logic (positions on issues)logic (positions on issues) Alternative views of preference: Alternative views of preference:

Learned (reinforcement, “locked in a closet” story) Learned (reinforcement, “locked in a closet” story) ““Discovered” (Plott, implies path-independence)Discovered” (Plott, implies path-independence)

Hybrid view: Combination of predisposition (e.g., language, Hybrid view: Combination of predisposition (e.g., language, “preparedness”), learning and logic“preparedness”), learning and logic

““Constructed” preference: effectsConstructed” preference: effects Context-dependence (comparative)Context-dependence (comparative) Description-dependent “framingDescription-dependent “framing

(descriptions guide attention) (descriptions guide attention) Reference-dependence (changes, not levels; Reference-dependence (changes, not levels;

anchoring)anchoring) Some values “protected”/sacred (health, Some values “protected”/sacred (health,

environment)environment) Is too much choice bad?Is too much choice bad? Open questions:Open questions:

Are effects smaller with familiar choices? Are effects smaller with familiar choices? Experts? Experts? Markets?Markets? New predictions (e.g. “big tip” labor supply experiment)New predictions (e.g. “big tip” labor supply experiment) Cross-species (pigeons, rats, capuchins)Cross-species (pigeons, rats, capuchins)

Preferences and utility theory: Preferences and utility theory: A guide for neuroscientistsA guide for neuroscientists

Colin Camerer, CaltechColin Camerer, Caltech Utility theory: numerical accounting for Utility theory: numerical accounting for

choiceschoices Bundles of goodsBundles of goods Risky and ambiguous “gambles” (EU, SEU)Risky and ambiguous “gambles” (EU, SEU) Choices over time (discounted utility)Choices over time (discounted utility)

Representation theorems:Representation theorems: Find mathematical structures that map onto Find mathematical structures that map onto

(“represent”) observable choices(“represent”) observable choices U(x) > U(y) iff x U(x) > U(y) iff x y y

numbersnumbers preferencespreferences

EU: Preferences over riskEU: Preferences over risk

How do people weigh and combine How do people weigh and combine likelihoods and outcomes? likelihoods and outcomes? GamblingGambling Risky investment (stocks, college, Risky investment (stocks, college,

mates)mates) InsuranceInsurance Social risks (terrorism, global warming)Social risks (terrorism, global warming)

Notation: f(x) is a risk with Notation: f(x) is a risk with probability f(x) of outcome xprobability f(x) of outcome x

Where utility theories come fromWhere utility theories come from AxiomaticAxiomatic

Decompose representations into logical “bones”Decompose representations into logical “bones” Find sets of axioms that are mathematically equivalent Find sets of axioms that are mathematically equivalent

to numerical representationsto numerical representations EmpiricalEmpirical

What mathematical functional forms fit choice data?What mathematical functional forms fit choice data? EvolutionaryEvolutionary

What preference structures would have adapted? (e.g., What preference structures would have adapted? (e.g., Robson JEcLit 01, JEcPers 02)Robson JEcLit 01, JEcPers 02)

NeuralNeural Do brain structures obey axioms?Do brain structures obey axioms?

Ideal: All four criteria should cohereIdeal: All four criteria should cohere

Possible decision rulesPossible decision rules MaximinMaximin

Choose risk with the best worst outcomeChoose risk with the best worst outcome f*=argmaxf*=argmaxg g [min[minx x x]x]

Safety-first/VARSafety-first/VAR Choose best EV with p(loss) below a thresholdChoose best EV with p(loss) below a threshold f*=argmaxf*=argmaxg g ΣΣxxxg(x) subject to xg(x) subject to ΣΣx<0 x<0 g(x)g(x)<<p*p*

Mean-varianceMean-variance Prefer high EV, low variancePrefer high EV, low variance f*=argmaxf*=argmaxgg E(g)-b E(g)-bσσ22(g)(g)

Expected utility Expected utility Choose risk with highest probability-averaged Choose risk with highest probability-averaged

outcome utilityoutcome utility f*=argmaxf*=argmaxg g ΣΣxxg(x)u(x)g(x)u(x)

The rise (and fall?) of expected utilityThe rise (and fall?) of expected utility Why EU?Why EU?

EV-maximization EV-maximization ΣΣxxxg(x) easily disproved xg(x) easily disproved St. Petersburg paradox St. Petersburg paradox

……but EU is a simple generalization of EVbut EU is a simple generalization of EV Axioms: Axioms:

Completeness of preference (including transitivity)Completeness of preference (including transitivity) Continuity (“solvability”) Continuity (“solvability”)

If fIf fggh then there exists p such that pf+(1-p)hh then there exists p such that pf+(1-p)hg g Cancellation (independence)Cancellation (independence)

If fIf fg then pf+(1-p)z g then pf+(1-p)z pg+(1-p)z for all z, p>0 pg+(1-p)z for all z, p>0

Axioms imply EU form U(g)=Axioms imply EU form U(g)=ΣΣxxu(x)g(x) u(x)g(x) Degree of risk-aversion: -u’’(x)/u’(x) (Arrow-Degree of risk-aversion: -u’’(x)/u’(x) (Arrow-

Pratt)Pratt)

What’s wrong with the axiomatic approachWhat’s wrong with the axiomatic approach Axioms are useful if they are more Axioms are useful if they are more

transparenttransparent than equivalent than equivalent representations representations

Easier to judge normative content than Easier to judge normative content than descriptivedescriptive

Is generality a seductive illusion?Is generality a seductive illusion? Thou shalt not killThou shalt not kill Always cancel common consequencesAlways cancel common consequences Always tell the truthAlways tell the truth

Competing axioms are difficult to compareCompeting axioms are difficult to compare E.g. independence versus betweeness E.g. independence versus betweeness

if if ffg then fg then f pf+(1-p)g pf+(1-p)g g for all 1>p>0 g for all 1>p>0

Cancellation is logically sensible but Cancellation is logically sensible but perceptually unnaturalperceptually unnatural

Allais common consequence problem:Allais common consequence problem: A: $1 M or? (.10, $5 M; .89, $1 M; .01, 0)A: $1 M or? (.10, $5 M; .89, $1 M; .01, 0) B: (.11, $1 M; .89,0) or? (.10,$5 M; .89,0; .01, 0)B: (.11, $1 M; .89,0) or? (.10,$5 M; .89,0; .01, 0)

Cancellation is logically sensible but Cancellation is logically sensible but perceptually unnaturalperceptually unnatural

Allais common consequence problem:Allais common consequence problem: A: A: $1 M$1 M or? (10, $5 M; .89, $1 M; .01, 0) or? (10, $5 M; .89, $1 M; .01, 0) B: (.11, $1 M; .89,0) or? B: (.11, $1 M; .89,0) or? (.10,$5 M; .89,0; .01, (.10,$5 M; .89,0; .01,

0)0)

Majority choose $1M in AMajority choose $1M in Aand (.10,$5M) in Band (.10,$5M) in B

Violates EUViolates EU A pair is (.11,$1M) or (.10,$5M) with common (.89,$1M)A pair is (.11,$1M) or (.10,$5M) with common (.89,$1M) B pair is (.11,$1M) or (.10,$5M) with common (.89,0)B pair is (.11,$1M) or (.10,$5M) with common (.89,0)

Cancellation is logically sensible but Cancellation is logically sensible but perceptually unnaturalperceptually unnatural

Allais common consequence problem:Allais common consequence problem: A: $1 M or? (10, $5 M; .89, $1 M; .01, 0)A: $1 M or? (10, $5 M; .89, $1 M; .01, 0) B: (.11, $1 M; .89,0) or? (.10,$5 M; .89,0; .01, 0)B: (.11, $1 M; .89,0) or? (.10,$5 M; .89,0; .01, 0) A’: (.11,$1M; .89, $1M) or? (.10, $5 M; .89, $1 A’: (.11,$1M; .89, $1M) or? (.10, $5 M; .89, $1

M; .01, 0)M; .01, 0) Brain craves whole gestalts, not Brain craves whole gestalts, not

decompositionsdecompositions

Compliance with axioms often depends Compliance with axioms often depends on unnatural representationson unnatural representations

58% choose C over D 58% choose C over D Sensible? Sensible?

Source: Kahneman-Tversky JBus 86Source: Kahneman-Tversky JBus 86

Axioms require unnatural representationsAxioms require unnatural representations BUT! D “first-order stochastically dominates” C (FOSD) BUT! D “first-order stochastically dominates” C (FOSD) A and B rearrange C and D to make dominance transparentA and B rearrange C and D to make dominance transparent KT: B chosen 100%, D chosen 42%KT: B chosen 100%, D chosen 42% FOSD is only detectableFOSD is only detectable if a table is constructed (or if a table is constructed (or

compare CDF’s). compare CDF’s). Mas-Collel: But they would be fired!”Mas-Collel: But they would be fired!”

Choice is a psychological processChoice is a psychological processWill depend on many factorsWill depend on many factors

Description-invariance (framing, reference-Description-invariance (framing, reference-dependence)dependence)

Actual study with n=792 docs (Harvard Med, Actual study with n=792 docs (Harvard Med, Brigham &Women’s, Hebrew U; McNeil et al JAMA Brigham &Women’s, Hebrew U; McNeil et al JAMA ’80s)’80s)

treatment 1 yr treatment 1 yr 5 yrs5 yrs choicechoice Surgery 10% 32% 66%Surgery 10% 32% 66% 53%53% Radiation 0% 23% 78% Radiation 0% 23% 78% 47%47%

treatment 1 yr treatment 1 yr 5 yrs5 yrs choicechoice both frames both frames Surgery 90% 68% 34%Surgery 90% 68% 34% 82%82% 60%60% Radiation 100% 77% 22% Radiation 100% 77% 22% 18%18% 40% 40%

Choice is a psychological processChoice is a psychological process Procedure-invariance (pref. reversal)Procedure-invariance (pref. reversal)

PreferPrefer p-bet (.95, $4) over $ bet (.30,$16) p-bet (.95, $4) over $ bet (.30,$16)……but price p-bet higherbut price p-bet higher

Context-invarianceContext-invariance Disappointment (across states [columns])Disappointment (across states [columns]) Regret (between choices [rows]) Regret (between choices [rows])

1/31/3 1/31/3 1/31/3A 10A 10 0 0 5 5B 0B 0 5+e 5+e 1010

Is regret an overadapted learning signal? Is regret an overadapted learning signal? (Gilovich-Medvec Olympic medalists (Gilovich-Medvec Olympic medalists study)study)

Many variants of expected utilityMany variants of expected utility

Source: Camerer JRiskUnc 88, Edwards (Ed) Source: Camerer JRiskUnc 88, Edwards (Ed) Utility TheoriesUtility Theories, 92, 92

Useful tool: Marschak-Machina triangle for Useful tool: Marschak-Machina triangle for representing 3-outcome gamblesrepresenting 3-outcome gambles

Outcomes Outcomes x3>x2>x1x3>x2>x1

Each point is a Each point is a gamblegamble

Theories Theories dictate dictate indifference indifference curve shapecurve shape

EU is equivalent toEU is equivalent to Linear indiff curvesLinear indiff curves ParallelParallel

Allais common Allais common consequence consequence effecteffect curves get curves get steeper toward steeper toward upper leftupper left

Different theories predict different Different theories predict different indifference mapsindifference maps

Facts from experimental studies:Facts from experimental studies: Betweenness (linear indiff curves) oftenBetweenness (linear indiff curves) often

violated violated (Prelec, 90 JRU, Camerer-Ho JRU 94):(Prelec, 90 JRU, Camerer-Ho JRU 94): If you prefer (.34,$20k) If you prefer (.34,$20k) (.17,$30k) (.17,$30k)

……should prefer (.34,$20k) to any mixture should prefer (.34,$20k) to any mixture

But most pick (.01,$30k.;.32,$20k) But most pick (.01,$30k.;.32,$20k) (.32,$20k)(.32,$20k)

Sensitive to compound lottery reduction Sensitive to compound lottery reduction thoughthough

More facts from experimentsMore facts from experiments

Violations are larger when some Violations are larger when some probabilities are low [inside the triangle] probabilities are low [inside the triangle] nonlinear w(p) is crucialnonlinear w(p) is crucial

Animal behavior (rats) similar to humans Animal behavior (rats) similar to humans (Kagel et al)(Kagel et al)

Small effect of experimental stakesSmall effect of experimental stakes Paying real money reduces noise, creates morePaying real money reduces noise, creates more

significantsignificant EU violations EU violations

Source: Camerer, 95; Harless-Camerer 94 EconometricaSource: Camerer, 95; Harless-Camerer 94 Econometrica

Prospect theory, I Prospect theory, I Key features:Key features:

Reference-dependence, nonlinear w(p)Reference-dependence, nonlinear w(p) Nonlinear weighting of probabilityNonlinear weighting of probability

Zeckhauser bullet example, 6Zeckhauser bullet example, 6 5 and 1 5 and 1 0 0 Inflection (sensitivity), elevation (risk attitude)Inflection (sensitivity), elevation (risk attitude) KT (’92 JRU) w(p)=pKT (’92 JRU) w(p)=pγγ///(p/(pγγ+(1-p)+(1-p)γγ))1/1/γγ

Prelec (98 E’metrica) w(p)=1/exp((ln(1/p)Prelec (98 E’metrica) w(p)=1/exp((ln(1/p)γγ) ) Large overweighting of low probabilitiesLarge overweighting of low probabilities γγ=.7 w(1/10)=.165, w(1/100)=.05, =.7 w(1/10)=.165, w(1/100)=.05,

w(1/1,000,000)=.002w(1/1,000,000)=.002 Morgenstern 79 J Ec Lit:Morgenstern 79 J Ec Lit:

[Like Newtonian mechanics] The domain of our axioms on utility [Like Newtonian mechanics] The domain of our axioms on utility theory is also restricted…For example, the probabilities used theory is also restricted…For example, the probabilities used must be within certain plausible ranges and not go to .01 or even must be within certain plausible ranges and not go to .01 or even less to .001, then be compared with other equally tiny numbers less to .001, then be compared with other equally tiny numbers such as .02 etc.”such as .02 etc.”

Prospect theory value function: Prospect theory value function: Note kink at zero and diminishing marginal sensitivity Note kink at zero and diminishing marginal sensitivity

(concave for x>0, convex for x<0)(concave for x>0, convex for x<0)

Empirical weighting functionsEmpirical weighting functions

SEU: Ambiguity and riskSEU: Ambiguity and risk Derive subjective (“personal”) probabilities Derive subjective (“personal”) probabilities

from bets between “states” s from bets between “states” s SEU form is SEU form is ΣΣssu(x(s))p(s) u(x(s))p(s) Ellsberg paradox: Ellsberg paradox:

p(s) cannot express both likelihood and p(s) cannot express both likelihood and “weight of evidence” or ambiguity“weight of evidence” or ambiguity

(One) resolution: p(A)+p(not-A) < 1(One) resolution: p(A)+p(not-A) < 1 P(A)/p(not-A) is likelihooodP(A)/p(not-A) is likelihoood 1-p(A)-p(not-A) is reserved belief 1-p(A)-p(not-A) is reserved belief

Caution: Updating given new information Caution: Updating given new information is tricky…is tricky…

Ambiguity-aversion Ambiguity-aversion with knowledge questionswith knowledge questions

1. Ambiguity Aversion (with Ming Hsu et al)1. Ambiguity Aversion (with Ming Hsu et al) Ambiguity is uncertainty about probability, Ambiguity is uncertainty about probability,

created by missing information that is relevant created by missing information that is relevant and could be knownand could be known

Does “weight of evidence”/ambiguity matter?Does “weight of evidence”/ambiguity matter? Longstanding debateLongstanding debate

Savage: NoSavage: No Logic overrides discomfort of not knowingLogic overrides discomfort of not knowing

Keynes, Knight, Ellsberg, experiments: YesKeynes, Knight, Ellsberg, experiments: Yes Many new theories (Gilboa-Schmeidler et al)Many new theories (Gilboa-Schmeidler et al)

Pessimism over Pessimism over setssets of beliefs of beliefs Nonadditive beliefs (“missing” probability is Nonadditive beliefs (“missing” probability is

“reserved belief”)“reserved belief”)

Historical suggestion: Distinct neural Historical suggestion: Distinct neural processes in ambiguity vs riskprocesses in ambiguity vs risk

"But if certain uncertainties in the problem were in "But if certain uncertainties in the problem were in cloudycloudy

or fuzzy form, then very often there was a shifting of or fuzzy form, then very often there was a shifting of gearsgears

and no effort at all was made to think deliberately andand no effort at all was made to think deliberately and

reflectively about the problem. Systematic reflectively about the problem. Systematic decomposition ofdecomposition of

the problem was shunned and an over-all 'seat of the the problem was shunned and an over-all 'seat of the pants'pants'

judgment was made which graphically reflected the judgment was made which graphically reflected the temperament of the decision maker.“ (Raiffa, 1963)temperament of the decision maker.“ (Raiffa, 1963)

Ambiguity vs risk is important in social scienceAmbiguity vs risk is important in social science Home bias in equity markets (1-2%/yr), Home bias in equity markets (1-2%/yr),

insurance, incomplete contracting, insurance, incomplete contracting, entrepreneurship, “rolloff” in voting, political entrepreneurship, “rolloff” in voting, political incumbency advantage, brand loyalty, law incumbency advantage, brand loyalty, law (“not proven” in Scottish law), game theory(“not proven” in Scottish law), game theory

Ambiguity-aversion Ambiguity-aversion pure demand for pure demand for information information even if it doesn’t affect a decisioneven if it doesn’t affect a decision

E.g. medical overtesting, “sunshine laws” in politicsE.g. medical overtesting, “sunshine laws” in politics Inflames hindsight bias in manager-worker Inflames hindsight bias in manager-worker

“agency” relationships“agency” relationships Permits encoding bias:Permits encoding bias:

US Senate Iraq report; “…led intelligence community US Senate Iraq report; “…led intelligence community to interpret to interpret ambiguousambiguous evidence as conclusive of a evidence as conclusive of a WMD program…”; Bush: “it might come in the form WMD program…”; Bush: “it might come in the form of a mushroom cloud”of a mushroom cloud”

Ambiguity-aversion as emotion-driven pessimismAmbiguity-aversion as emotion-driven pessimism

Risk case: Risk case: P(red)=P(blue)=.5P(red)=P(blue)=.5

Ambiguous case Ambiguous case w(red)=w(blue) but don’t add to 1w(red)=w(blue) but don’t add to 1 1-w(red)-w(blue) is “reserved belief” 1-w(red)-w(blue) is “reserved belief” ……a “vigilance” signal expressed by limbic system?a “vigilance” signal expressed by limbic system? Bet on red is valued Bet on red is valued

w(red)u($10)= P(red)u($10) - [P(red)-w(red)]u($10)w(red)u($10)= P(red)u($10) - [P(red)-w(red)]u($10) risky part pessimismrisky part pessimism

look for neural dissociation look for neural dissociation Measure strength of ambiguity aversion by Measure strength of ambiguity aversion by

w(red)=P(red)w(red)=P(red)γγ

γγ>1 ambiguity-aversion, >1 ambiguity-aversion, γ γ=1 neutrality=1 neutrality γ γ Logit “softmax” model Logit “softmax” model P(bet red>x)=1/(1+exp[P(bet red>x)=1/(1+exp[λλ*[x*[xρρ-10-10ρρP(red)P(red)γγ]])]])

Description-dependent “framing” (descriptions Description-dependent “framing” (descriptions guide attention)guide attention)

Analogy to figure-ground in perceptionAnalogy to figure-ground in perception Actual study with n=792 docs (Harvard Med, Actual study with n=792 docs (Harvard Med,

Brigham &Women’s, Hebrew U; McNeil et al Brigham &Women’s, Hebrew U; McNeil et al JAMA ’80s)JAMA ’80s)

treatment 1 yr 5 yrstreatment 1 yr 5 yrs choicechoice Surgery 10% 32% 66%Surgery 10% 32% 66% 53%53% Radiation 0% 23% 78% Radiation 0% 23% 78% 47%47%

treatment 1 yr 5 yrstreatment 1 yr 5 yrs choicechoice both frames both frames Surgery 90% 68% 34%Surgery 90% 68% 34% 82% 82% 60% 60% Radiation 100% 77% 22% Radiation 100% 77% 22% 18% 40% 18% 40%

Asian disease problem (-200 vs (1/3) of -600 / +400 vs (2/3) Asian disease problem (-200 vs (1/3) of -600 / +400 vs (2/3) 600600

Pro-choice vs pro-lifePro-choice vs pro-life Politics: “spin” (Lakoff)Politics: “spin” (Lakoff)

e.g. aren’t we better off w/ Hussein gone? e.g. aren’t we better off w/ Hussein gone? Liberation vs. occupationLiberation vs. occupation ……other examples? other examples?

Supply-side response: Competitive framing; which frame Supply-side response: Competitive framing; which frame “wins”?“wins”?

Some new frontiersSome new frontiers Animal model Animal model

Animals exhibit all EU violations humans Animals exhibit all EU violations humans dodo

Field studiesField studies Imagined vs. learned probabilities Imagined vs. learned probabilities

(Erev, Weber et al Psych Sci)(Erev, Weber et al Psych Sci)

Emotion and nonlinear w(p) Emotion and nonlinear w(p) (Hsee-(Hsee-Rottenstreich Psych Sci)Rottenstreich Psych Sci)

Neural foundationsNeural foundations

Prospect theory, I Prospect theory, I

Key features:Key features: Reference-dependence, nonlinear w(p)Reference-dependence, nonlinear w(p)

Reference-dependenceReference-dependence Extension of psychophysics (e.g. hot-cold)Extension of psychophysics (e.g. hot-cold) U(x-r)U(x-r) U(.) “reflects” (gamble over losses)U(.) “reflects” (gamble over losses)

Loss-aversionLoss-aversion Q: Is loss-aversion a preference or a forecasting Q: Is loss-aversion a preference or a forecasting

mistakes (underestimates emotional “immunity” a la mistakes (underestimates emotional “immunity” a la Tim Wilson-Dan Gilbert)? Tim Wilson-Dan Gilbert)?

Loss-aversion in savings decisionsLoss-aversion in savings decisions(note few points with y-axis actual utility <0)(note few points with y-axis actual utility <0) Chua & Camerer 03 Chua & Camerer 03

Actual Utility Vs Optimal Utility

-50

-40

-30

-20

-10

0

10

20

30

40

50

-50 -30 -10 10 30 50

Optimal Utility Gains/Losses

Act

ual

Uti

lity

Gai

ns/

Lo

sses

Data Points Jack Knife Regression

g

Reference-dependence modellingReference-dependence modelling (Koszegi-Rabin, 05)(Koszegi-Rabin, 05) Two problems in prospect theory:Two problems in prospect theory:

Is v(c-r) the Is v(c-r) the onlyonly carrier of utility? Probably not… carrier of utility? Probably not… How is r “chosen”? Perceptual? Expectations? How are How is r “chosen”? Perceptual? Expectations? How are

expectations chosen? expectations chosen? KR solutionKR solution

U(c|r)= m(c)+U(c|r)= m(c)+µµ(m(c)-m(r)) (m(c)-m(r)) separable into consumption separable into consumption and “surprise” utility and “surprise” utility

For distributions F, F*=argmaxFor distributions F, F*=argmaxFF∫∫ccu(c|r)dF(c)u(c|r)dF(c) For reference distribution G, F*=argmaxFor reference distribution G, F*=argmaxFF∫∫cc∫∫rru(c|r)dF(c)dG(r)u(c|r)dF(c)dG(r)

Axioms:Axioms: A0: A0: µ(x) continuous, twice differentiable (for x≠0), µ(0)=0µ(x) continuous, twice differentiable (for x≠0), µ(0)=0 A1: A1: µ(x) strictly increasing (µ’(x)>0)µ(x) strictly increasing (µ’(x)>0) A2: If y>x>0, then A2: If y>x>0, then µ(y)+µ(-y)<µ(x)+µ(-x) µ(y)+µ(-y)<µ(x)+µ(-x)

(convexity of disutility is weaker than concavity of utility)(convexity of disutility is weaker than concavity of utility) A3: A3: µ’’(x)≤0 for x>0 and µ’’(x)≥0 for x<0 µ’’(x)≤0 for x>0 and µ’’(x)≥0 for x<0 (reflection (reflection

effect)effect) A3’: For all x≠0, µ’’(x)=0 A3’: For all x≠0, µ’’(x)=0 (piecewise (piecewise

linear utility)linear utility) A4: limA4: limx-->0x-->0 µ’(-|x|) / lim µ’(-|x|) / limx-->0x-->0 µ’(|x|) = µ’(|x|) = λλ > 1 (coef. of loss- > 1 (coef. of loss-

aversion)aversion)

Economic domainEconomic domain citation(s)citation(s) Type of dataType of data Estimate Estimate λλ

Instant endowment effects for goodsInstant endowment effects for goods Kahneman-Knetsch-Thaler Kahneman-Knetsch-Thaler (1990)(1990)

Field data (survey), goods Field data (survey), goods experimentsexperiments

2.292.29

Choices over money gamblesChoices over money gambles Kahneman and Tversky Kahneman and Tversky (1992)(1992)

Choice experimentsChoice experiments 2.252.25

Asymmetric price elasticities for consumer Asymmetric price elasticities for consumer product increases & decreasesproduct increases & decreases

Putler (1992), Hardie-Putler (1992), Hardie-Fader-Johnson (1993)Fader-Johnson (1993)

Supermarket scanner dataSupermarket scanner data 2.40, 2.40, 1.631.63

Loss-aversion for goods relative to moneyLoss-aversion for goods relative to money Bateman et al (2004) ADD Bateman et al (2004) ADD NAMESNAMES

Choice experimentsChoice experiments 1.301.30

Loss-aversion relative to initial seller “offer”Loss-aversion relative to initial seller “offer” Chen, Lakshminarayanan, Chen, Lakshminarayanan, Santos (2005)Santos (2005)

Capuchin monkeys trading tokens Capuchin monkeys trading tokens for stochastic food rewardsfor stochastic food rewards

2.702.70

Reference-dependence in two-part distribution Reference-dependence in two-part distribution channel pricingchannel pricing

Ho-Zhang (2005)Ho-Zhang (2005) Bargaining experimentsBargaining experiments 2.712.71

Aversion to losses from international tradeAversion to losses from international trade Tovar (2005) Tovar (2005) Non-tariff trade barriers, US 1983Non-tariff trade barriers, US 1983 1.95-1.95-2.392.39

Surprisingly few announcements of negative Surprisingly few announcements of negative EPS and negative year-to-year EPS EPS and negative year-to-year EPS changeschanges

DeGeorge, Patel and DeGeorge, Patel and Zeckhauser (1999)Zeckhauser (1999)

Earnings per share (EPS) changes Earnings per share (EPS) changes from year to year for US firmsfrom year to year for US firms

Disposition effects in housingDisposition effects in housing Genesove & Mayer (2001)Genesove & Mayer (2001) Boston condo prices 1990-97Boston condo prices 1990-97

Disposition effects in stocksDisposition effects in stocks Odean (1998)Odean (1998) Individual investor stock tradesIndividual investor stock trades

Disposition effects in stocksDisposition effects in stocks Weber and Camerer Weber and Camerer (1999)(1999)

Stock trading experimentsStock trading experiments

Daily income targeting by NYC cab driversDaily income targeting by NYC cab drivers Camerer-Babcock-Camerer-Babcock-Loewenstein-Thaler Loewenstein-Thaler (1997)(1997)

Daily hours-wages observations Daily hours-wages observations (three data sets)(three data sets)

Equity premium puzzleEquity premium puzzle Benartzi-Thaler (1997)Benartzi-Thaler (1997) US stock returnsUS stock returns

Consumption: Aversion to period utility lossConsumption: Aversion to period utility loss Chua and Camerer (2004)Chua and Camerer (2004) Savings-consumption experimentsSavings-consumption experiments

Monkey loss-aversionMonkey loss-aversion (a,b,c) means display (a,b,c) means display

a, then pay b or ca, then pay b or c One: stochastic One: stochastic

dominancedominance Two: reference-Two: reference-

dependence (risky)dependence (risky) Three: reference-Three: reference-

dependence (riskless)dependence (riskless)

Reference-dependenceReference-dependence Sensations depend on reference points rSensations depend on reference points r

E.g. put two hands in separate hot and cold water, E.g. put two hands in separate hot and cold water, then in one large warm baththen in one large warm bath

Hot hand feels colder and the cold hand feels hotter Hot hand feels colder and the cold hand feels hotter Loss-aversion Loss-aversion ≡ -v(-x) > v(x) for x>0 (KT 79)≡ -v(-x) > v(x) for x>0 (KT 79)

Or v’(x)|Or v’(x)|++ < v’(x) | < v’(x) |- - …a “kink” at 0; “first-order risk-…a “kink” at 0; “first-order risk-aversion” aka focussing illusion?aversion” aka focussing illusion?

Requires theory of “mental accounting”Requires theory of “mental accounting” What gains/losses are grouped together?What gains/losses are grouped together? When are mental accounts closed/opened?When are mental accounts closed/opened? Conjecture: time, space, cognitive boundaries Conjecture: time, space, cognitive boundaries

mattermatter Example: Last-race-of-the-day effect (bets switch to Example: Last-race-of-the-day effect (bets switch to

longshots to “break even”, McGlothlin 1956)longshots to “break even”, McGlothlin 1956)

Reference-dependence modellingReference-dependence modelling (Koszegi-Rabin, 05)(Koszegi-Rabin, 05)

Prop 1: If µ satisfies A0-A4, then Prop 1: If µ satisfies A0-A4, then “reference point preference” follows“reference point preference” follows (If A3’), then for F and F’, U(F|F’) ≥U(F’|F’) (If A3’), then for F and F’, U(F|F’) ≥U(F’|F’)

U(F|F) ≥U(F’|F) U(F|F) ≥U(F’|F) Big move: What is reference distribution? Big move: What is reference distribution?

Impose “personal equilibrium”: r=F* Impose “personal equilibrium”: r=F* Pro: Ties reference point to expected actionsPro: Ties reference point to expected actions Con: If µ(x) is a “prediction error” designed for Con: If µ(x) is a “prediction error” designed for

learning, r=F* means there is nothing to learn learning, r=F* means there is nothing to learn Implication: Can get multiple equilibria Implication: Can get multiple equilibria

(buy if you plan to buy, don’t buy if you (buy if you plan to buy, don’t buy if you don’t)don’t) Role for framing/advertising etc. in choosing an Role for framing/advertising etc. in choosing an

equilibrium (supply side response)equilibrium (supply side response)

Endowment effects (KKT JPE ’90)Endowment effects (KKT JPE ’90)

KKT “mugs” experiment (JPE ‘90)KKT “mugs” experiment (JPE ‘90)

Reference-dependence and Reference-dependence and endowment effectsendowment effects

Koszegi-Rabin applied to pens (xKoszegi-Rabin applied to pens (xpp), $ (x), $ (xdd)) Utility is direct plus “transition utility” Utility is direct plus “transition utility”

t(.)t(.)

ωω is weight on ref-dependent utility, is weight on ref-dependent utility, λλ is is strength of loss-aversion strength of loss-aversion

)()(),;,( dpdpdpdp ytytxbxyyxxu

,0 if |)(|

,0 if )()(

pp p

ppp

p yybωyv

yybωyvyt

Endowment effects analysisEndowment effects analysis Choosing (choice-equivalent Choosing (choice-equivalent PPcc))

Reference points r(p)=r(d)=0Reference points r(p)=r(d)=0 U(gain pen)=b+U(gain pen)=b+ωωb U(gain Pb U(gain Pcc)= P)= Pcc+ + ωωPPcc

Equating gives PEquating gives Pcc=b=b Selling (selling price PSelling (selling price Pss))

Reference points r(p)=b, r(d)=0Reference points r(p)=b, r(d)=0 U(“lose” pen, gain $)U(“lose” pen, gain $) U(keep pen, gain 0)= bU(keep pen, gain 0)= b Equating gives PEquating gives Pss==

Buying price PBuying price Pbb = =

Prices ordered by PPrices ordered by Pss>P>Pc c >P>Pbb iff iff λλ, , ωω>0>0

SS PbP 1

1

)1(b

1

)1(b

Plott-Zeiler reviewPlott-Zeiler review

Data from young (PCC) and old (80 yr olds) using Data from young (PCC) and old (80 yr olds) using PZ instructions (Kovalchik et al JEBO in press 04)PZ instructions (Kovalchik et al JEBO in press 04)

Plott-Zeiler (AER 05) results: Plott-Zeiler (AER 05) results: replication (top) vs mugs-first (bottom)replication (top) vs mugs-first (bottom)

““Status quo bias” and defaults in organ Status quo bias” and defaults in organ donation (Johnson-Goldstein Sci 03)donation (Johnson-Goldstein Sci 03)

Disposition effects in housing (Genesove and Disposition effects in housing (Genesove and Mayer, 2001)Mayer, 2001)

Why is housing important? Why is housing important? It's big: It's big:

Residential real estate $ value is close to stock market value.Residential real estate $ value is close to stock market value. It’s likely that limited rationality persistsIt’s likely that limited rationality persists

most people buy houses rarely (don't learn from experience). most people buy houses rarely (don't learn from experience). Very emotional ("I fell in love with that house"). Very emotional ("I fell in love with that house"). House purchases are "big, rare" decisions -- mating, kids, House purchases are "big, rare" decisions -- mating, kids,

education, jobseducation, jobs Advice market may not correct errors Advice market may not correct errors buyer and seller agents typically paid a fixed % of $ price (Steve buyer and seller agents typically paid a fixed % of $ price (Steve

Levitt study shows agents sell their own houses more slowly and Levitt study shows agents sell their own houses more slowly and get more $). get more $).

Claim: Claim: People hate selling their houses at a "loss" from People hate selling their houses at a "loss" from nominalnominal [not [not

inflation-adjusted!] original purchase price. inflation-adjusted!] original purchase price.

Boston condo slump in nominal pricesBoston condo slump in nominal prices

G-M econometric modelG-M econometric model

Model: Listing price L_ist depends on “hedonic terms” and m*Loss_ist(m=0 is no disposition effect)

…but *measured* LOSS_ist excludes unobserved quality v_i…so the error term η_it contains true error and unobserved quality v_i …causes upward bias in measurement of m Intuitively: If a house has a great unobserved quality v_i, the purchase price P^0_is will be too high relative to the regression. The model will think that somebody who refused to cut their price is being loss-averse whereas they are really just pricing to capture the unobserved component of value.

Results: m is significant, smaller for investors (not Results: m is significant, smaller for investors (not owner-occupants; less “attachment”?)owner-occupants; less “attachment”?)

Cab driver “income targeting” Cab driver “income targeting” (Camerer et al QJE 97)(Camerer et al QJE 97)

Cab driver instrumental variables Cab driver instrumental variables (IV) showing experience effect (IV) showing experience effect

Capuchins obey law of demand Capuchins obey law of demand (K. Chen et al 05)(K. Chen et al 05)

““Arbitrary” valuationsArbitrary” valuations Stock prices?Stock prices? Wages (what are different jobs really Wages (what are different jobs really

worth?)worth?) Depends on value to firm (hard to measure)Depends on value to firm (hard to measure) & “compensating differentials/disutility (hard to & “compensating differentials/disutility (hard to

measure)measure) Exotic new productsExotic new products Housing (SFHousing (SF Pittsburgh tend to buy “too Pittsburgh tend to buy “too

much house”; Simonsohn and Loewenstein much house”; Simonsohn and Loewenstein 03)03)

Exec comp'n (govt e.g. $150k for senator, Exec comp'n (govt e.g. $150k for senator, vs CEO's, $38.5 million Britney Spears)vs CEO's, $38.5 million Britney Spears)

Anchored valuation: Valuations for listening to Anchored valuation: Valuations for listening to

poetry framed as labor (top) or leisure (bottom)poetry framed as labor (top) or leisure (bottom) (Ariely, Loewenstein, Prelec QJE 03 and working (Ariely, Loewenstein, Prelec QJE 03 and working

paperhttp://sds.hss.cmu.edu/faculty/Loewenstein/downloads/Sawyersubmitted.pdfpaperhttp://sds.hss.cmu.edu/faculty/Loewenstein/downloads/Sawyersubmitted.pdf

What econ. would happen if valuations are arbitrary?What econ. would happen if valuations are arbitrary?

Perfect competitionPerfect competition price=marginal cost…anchoring influences price=marginal cost…anchoring influences quantity,quantity, not price; expect large Q variations for similar not price; expect large Q variations for similar productsproducts

Attempts to influence the anchor (QVC home shopping, etc., "for Attempts to influence the anchor (QVC home shopping, etc., "for you just $59.95”). you just $59.95”).

Advertising!!!Advertising!!! If social comparison/imitation is an anchor, expect geographical, If social comparison/imitation is an anchor, expect geographical,

temporal, social clustering (see this in law & medical practice)temporal, social clustering (see this in law & medical practice) E.g., CEO pay linked to pay of Directors on Board's comp'n E.g., CEO pay linked to pay of Directors on Board's comp'n

committee. Geographical differences in housing prices, committee. Geographical differences in housing prices, London,Tokyo, NYC, SF. London,Tokyo, NYC, SF.

Interindustry wage differentials Interindustry wage differentials for the same work for the same work (Stanford (Stanford contracts out janitorial service so it doesn't have to pay as much; contracts out janitorial service so it doesn't have to pay as much; cf. airline security personnel??)cf. airline security personnel??)

Sports salaries: $100k/yr Miami Dolphins 1972 vs $10million/yr Sports salaries: $100k/yr Miami Dolphins 1972 vs $10million/yr modern footballmodern football

Huge rise in CEO comp'n from 1990 (42 times worker wage) to Huge rise in CEO comp'n from 1990 (42 times worker wage) to 2000 (531 times); big differentials between US and Europe2000 (531 times); big differentials between US and Europe

Consumers who are most anchorable or influenceable will be Consumers who are most anchorable or influenceable will be most faddish -- children and toys!!? (McDonald's happy meal etc)most faddish -- children and toys!!? (McDonald's happy meal etc)

1/n heuristic & partition dependence in the lab 1/n heuristic & partition dependence in the lab (cf. “corporate socialism”, Scharfstein & Stein, at corporate level)(cf. “corporate socialism”, Scharfstein & Stein, at corporate level)

Experimental markets & prob judgmentExperimental markets & prob judgment

1. Abstract stimuli vs natural events??1. Abstract stimuli vs natural events?? pro: can precisely control information of individualspro: can precisely control information of individuals can conpute a Bayesian predictioncan conpute a Bayesian prediction con: maybe be fundamentally different mechanisms than for concrete con: maybe be fundamentally different mechanisms than for concrete

events...events... 2. Do markets eliminate biases?2. Do markets eliminate biases? Yes: specializationYes: specialization

Market is a dollar-weighted average opinionMarket is a dollar-weighted average opinion Uninformed traders follow informed onesUninformed traders follow informed ones Bankruptcy Bankruptcy

No: Short-selling constraintsNo: Short-selling constraints Confidence (and trade size) uncorrelated with informationConfidence (and trade size) uncorrelated with information Camerer (1987): Experience reduces pricing biases but *increases* Camerer (1987): Experience reduces pricing biases but *increases*

allocation biasesallocation biases Contingent claims markets:Contingent claims markets: Markets enforce correct prices..BUT probability judgment Markets enforce correct prices..BUT probability judgment

influences allocations and volume of trade influences allocations and volume of trade (example: Iowa political (example: Iowa political markets)markets)

Choice-aversion Choice-aversion How to model “too much choice”? How to model “too much choice”?

Anticipated regret from making a mistakeAnticipated regret from making a mistake ““grass is greener”/buyer’s remorsegrass is greener”/buyer’s remorse Direct disutility for too-large choice set (e.g. too Direct disutility for too-large choice set (e.g. too

complex)complex) Policy question: Policy question:

Markets are good at Markets are good at expandingexpanding choice…what is a good choice…what is a good institution for limiting choice? institution for limiting choice?

Example: Bottled water in supermarketsExample: Bottled water in supermarkets Limit “useless” substitution? What is the right amount? Limit “useless” substitution? What is the right amount? Pro-govt example: Swedish privatized social securityPro-govt example: Swedish privatized social security

Offered hundreds of fundsOffered hundreds of funds Default fund is low-fee global index (not too popular)Default fund is low-fee global index (not too popular) Most popular fund is local tech, down 80% 1Most popular fund is local tech, down 80% 1stst yr yr

Is too much choice bad? Is too much choice bad? Jams study (Iyengar-Lepper):Jams study (Iyengar-Lepper):

6 jams6 jams 40% stopped, 30% purchased40% stopped, 30% purchased 24 jams24 jams 60% stopped, 3% purchased60% stopped, 3% purchased

Assignment study: Assignment study: Short listShort list 74% did the extra credit assignment74% did the extra credit assignment Long listLong list 60% did the extra credit assignment60% did the extra credit assignment

Participation in 401(k) goes down 2% for every 10 extra funds Participation in 401(k) goes down 2% for every 10 extra funds Shoe salesman: Never show more than 3 pairs of shoes…Shoe salesman: Never show more than 3 pairs of shoes… Medical Medical

65% of nonpatients said they would want to be in charge of 65% of nonpatients said they would want to be in charge of medical treatment…but only12% of ex-cancer patients said they medical treatment…but only12% of ex-cancer patients said they wouldwould

Camerer conjecture: The curse of the compositeCamerer conjecture: The curse of the composite Paraphrased personals ad: “I want a man with the good looks of Paraphrased personals ad: “I want a man with the good looks of

Brad Pitt, the compassion of Denzel Washington…”Brad Pitt, the compassion of Denzel Washington…” Is there “too much” mate choice in big cities? Is there “too much” mate choice in big cities?

IIlusions of transparencyIIlusions of transparency ““Curse of knowledge”Curse of knowledge” Difficult to recover coarse partition from fine-grained oneDifficult to recover coarse partition from fine-grained one Piaget example: New PhD’s teachingPiaget example: New PhD’s teaching EA Poe, “telltale heart”EA Poe, “telltale heart” Computer manualsComputer manuals “ “ The tapper” study (tapping out songs with a pencil)The tapper” study (tapping out songs with a pencil) Hindsight bias Hindsight bias Recollection of P_t(X) at t+1 biased by whether X occurredRecollection of P_t(X) at t+1 biased by whether X occurred ““I should have known!”I should have known!” ““You should have known” (“ignored warning signs”)You should have known” (“ignored warning signs”) --> juries in legal cases (securities cases)--> juries in legal cases (securities cases) implications for principal-agent relations? implications for principal-agent relations?

Spotlight effect (Tom Gilovich et al)Spotlight effect (Tom Gilovich et al) Eating/movies aloneEating/movies alone Wearing a Barry Manilow t-shirtWearing a Barry Manilow t-shirt psychology: Shows how much we think others are attending when psychology: Shows how much we think others are attending when

they’re notthey’re not

Some referencesSome references Camerer 1995 Handbook Expl EconCamerer 1995 Handbook Expl Econ Camerer & Harless 94 EconometricaCamerer & Harless 94 Econometrica Camerer 1989 JRiskUnc, Edwards 92 edited bookCamerer 1989 JRiskUnc, Edwards 92 edited book Camerer World Congress Ec’ic Society 05 (avail Camerer World Congress Ec’ic Society 05 (avail

11/05)11/05) John Hey chapter (Kreps-Wallis book) 97 (more pro-John Hey chapter (Kreps-Wallis book) 97 (more pro-

EU)EU) Starmer J Ec Lit 2002Starmer J Ec Lit 2002 John Quiggin, Duncan Luce 2000+ booksJohn Quiggin, Duncan Luce 2000+ books Annual Rev Psych articles on decision making Annual Rev Psych articles on decision making

(Shafir LeBoeuf 2000 et al)(Shafir LeBoeuf 2000 et al) Camerer Camerer Behavioral Game TheoryBehavioral Game Theory, Princeton, 2003, Princeton, 2003