“Constructed” preferences SS200 Colin Camerer

“Constructed” preferencesSS200 Colin Camerer • Preferences: “complete, transitive” u(x), tradeoffs among goods • Historical note: Axioms not empirically well-founded. They were designed to provide simple mathematical framework for aggregation (utility demand) and because Pareto won the “what is utility?” battle • “Constructed” suggests expression of preference is like problem-solving: • Will you vote for John Kerry? • Answered by rapid intuition (tall, good hair) and/or deliberate logic (positions on issues) • Alternative views of preference: • Learned (reinforcement, “locked in a closet” story) • “Discovered” (Plott, implies path-independence) • Hybrid view: Combination of predisposition (e.g., language, “preparedness”), learning and logic

“Constructed” preference: effects • Context-dependence (comparative) • Description-dependent “framing (descriptions guide attention) • Reference-dependence (changes, not levels; anchoring) • Some values “protected”/sacred (health, environment) • Is too much choice bad? • Open questions: • Are effects smaller with familiar choices? • Experts? • Markets? • New predictions (e.g. “big tip” labor supply experiment) • Cross-species (pigeons, rats, capuchins)

Preferences and utility theory: A guide for neuroscientistsColin Camerer, Caltech • Utility theory: numerical accounting for choices • Bundles of goods • Risky and ambiguous “gambles” (EU, SEU) • Choices over time (discounted utility) • Representation theorems: • Find mathematical structures that map onto (“represent”) observable choices • U(x) > U(y) iff x  y numbers preferences

EU: Preferences over risk • How do people weigh and combine likelihoods and outcomes? • Gambling • Risky investment (stocks, college, mates) • Insurance • Social risks (terrorism, global warming) • Notation: f(x) is a risk with probability f(x) of outcome x

Where utility theories come from • Axiomatic • Decompose representations into logical “bones” • Find sets of axioms that are mathematically equivalent to numerical representations • Empirical • What mathematical functional forms fit choice data? • Evolutionary • What preference structures would have adapted? (e.g., Robson JEcLit 01, JEcPers 02) • Neural • Do brain structures obey axioms? • Ideal: All four criteria should cohere

Possible decision rules • Maximin • Choose risk with the best worst outcome • f*=argmaxg [minx x] • Safety-first/VAR • Choose best EV with p(loss) below a threshold • f*=argmaxg Σxxg(x) subject to Σx<0 g(x)<p* • Mean-variance • Prefer high EV, low variance • f*=argmaxg E(g)-bσ2(g) • Expected utility • Choose risk with highest probability-averaged outcome utility • f*=argmaxg Σxg(x)u(x)

The rise (and fall?) of expected utility • Why EU? • EV-maximization Σxxg(x) easily disproved • St. Petersburg paradox …but EU is a simple generalization of EV • Axioms: • Completeness of preference (including transitivity) • Continuity (“solvability”) • If fgh then there exists p such that pf+(1-p)hg • Cancellation (independence) • If fg then pf+(1-p)z pg+(1-p)z for all z, p>0 • Axioms imply EU form U(g)=Σxu(x)g(x) • Degree of risk-aversion: -u’’(x)/u’(x) (Arrow-Pratt)

What’s wrong with the axiomatic approach • Axioms are useful if they are more transparent than equivalent representations • Easier to judge normative content than descriptive • Is generality a seductive illusion? • Thou shalt not kill • Always cancel common consequences • Always tell the truth • Competing axioms are difficult to compare • E.g. independence versus betweeness if fg then f pf+(1-p)g g for all 1>p>0

Cancellation is logically sensible but perceptually unnatural • Allais common consequence problem: • 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)

Cancellation is logically sensible but perceptually unnatural • Allais common consequence problem: • 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) • Majority choose $1M in A and (.10,$5M) in B • Violates EU • A pair is (.11,$1M) or (.10,$5M) with common (.89,$1M) • B pair is (.11,$1M) or (.10,$5M) with common (.89,0)

Cancellation is logically sensible but perceptually unnatural • Allais common consequence problem: • 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) • A’: (.11,$1M; .89, $1M) or? (.10, $5 M; .89, $1 M; .01, 0) • Brain craves whole gestalts, not decompositions

Compliance with axioms often depends on unnatural representations • 58% choose C over D • Sensible? • Source: Kahneman-Tversky JBus 86

Axioms require unnatural representations • BUT! D “first-order stochastically dominates” C (FOSD) • A and B rearrange C and D to make dominance transparent • KT: B chosen 100%, D chosen 42% • FOSD is only detectable if a table is constructed (or compare CDF’s). Mas-Collel: But they would be fired!”

Choice is a psychological processWill depend on many factors • Description-invariance (framing, reference-dependence) • Actual study with n=792 docs (Harvard Med, Brigham &Women’s, Hebrew U; McNeil et al JAMA ’80s) • treatment 1 yr 5 yrs choice • Surgery 10% 32% 66% 53% • Radiation 0% 23% 78% 47% • treatment 1 yr 5 yrs choice both frames • Surgery 90% 68% 34% 82% 60% • Radiation 100% 77% 22% 18% 40%

Choice is a psychological process • Procedure-invariance (pref. reversal) • Prefer p-bet (.95, $4) over $ bet (.30,$16) …but price p-bet higher • Context-invariance • Disappointment (across states [columns]) • Regret (between choices [rows]) 1/3 1/3 1/3 A 10 0 5 B 0 5+e 10 • Is regret an overadapted learning signal? (Gilovich-Medvec Olympic medalists study)

Many variants of expected utility • Source: Camerer JRiskUnc 88, Edwards (Ed) Utility Theories, 92

Useful tool: Marschak-Machina triangle for representing 3-outcome gambles • Outcomes x3>x2>x1 • Each point is a gamble • Theories dictate indifference curve shape

EU is equivalent to • Linear indiff curves • Parallel • Allais common consequence effect curves get steeper toward upper left

Different theories predict different indifference maps

Facts from experimental studies: • Betweenness (linear indiff curves) often violated (Prelec, 90 JRU, Camerer-Ho JRU 94): • If you prefer (.34,$20k)  (.17,$30k) …should prefer (.34,$20k) to any mixture But most pick (.01,$30k.;.32,$20k)  (.32,$20k) Sensitive to compound lottery reduction though

More facts from experiments • Violations are larger when some probabilities are low [inside the triangle]  nonlinear w(p) is crucial • Animal behavior (rats) similar to humans (Kagel et al) • Small effect of experimental stakes • Paying real money reduces noise, creates more significant EU violations • Source: Camerer, 95; Harless-Camerer 94 Econometrica

Prospect theory, I • Key features: • Reference-dependence, nonlinear w(p) • Nonlinear weighting of probability • Zeckhauser bullet example, 6 5 and 1 0 • Inflection (sensitivity), elevation (risk attitude) • KT (’92 JRU) w(p)=pγ//(pγ+(1-p)γ)1/γ • Prelec (98 E’metrica) w(p)=1/exp((ln(1/p)γ) • Large overweighting of low probabilities • γ=.7 w(1/10)=.165, w(1/100)=.05, w(1/1,000,000)=.002 • Morgenstern 79 J Ec Lit: • [Like Newtonian mechanics] The domain of our axioms on utility theory is also restricted…For example, the probabilities used must be within certain plausible ranges and not go to .01 or even less to .001, then be compared with other equally tiny numbers such as .02 etc.”

Prospect theory value function: Note kink at zero and diminishing marginal sensitivity (concave for x>0, convex for x<0)

Empirical weighting functions

SEU: Ambiguity and risk • Derive subjective (“personal”) probabilities from bets between “states” s • SEU form is Σsu(x(s))p(s) • Ellsberg paradox: • p(s) cannot express both likelihood and “weight of evidence” or ambiguity • (One) resolution: p(A)+p(not-A) < 1 • P(A)/p(not-A) is likelihoood • 1-p(A)-p(not-A) is reserved belief • Caution: Updating given new information is tricky…

Ambiguity-aversion with knowledge questions

1. Ambiguity Aversion (with Ming Hsu et al) • Ambiguity is uncertainty about probability, created by missing information that is relevant and could be known • Does “weight of evidence”/ambiguity matter? • Longstanding debate • Savage: No • Logic overrides discomfort of not knowing • Keynes, Knight, Ellsberg, experiments: Yes • Many new theories (Gilboa-Schmeidler et al) • Pessimism over sets of beliefs • Nonadditive beliefs (“missing” probability is “reserved belief”)

Historical suggestion: Distinct neural processes in ambiguity vs risk "But if certain uncertainties in the problem were in cloudy or fuzzy form, then very often there was a shifting of gears and no effort at all was made to think deliberately and reflectively about the problem. Systematic decomposition of the problem was shunned and an over-all 'seat of the pants' judgment was made which graphically reflected the temperament of the decision maker.“ (Raiffa, 1963)

Ambiguity vs risk is important in social science • Home bias in equity markets (1-2%/yr), insurance, incomplete contracting, entrepreneurship, “rolloff” in voting, political incumbency advantage, brand loyalty, law (“not proven” in Scottish law), game theory • Ambiguity-aversion  pure demand for information even if it doesn’t affect a decision • E.g. medical overtesting, “sunshine laws” in politics • Inflames hindsight bias in manager-worker “agency” relationships • Permits encoding bias: • US Senate Iraq report; “…led intelligence community to interpret ambiguous evidence as conclusive of a WMD program…”; Bush: “it might come in the form of a mushroom cloud”

Ambiguity-aversion as emotion-driven pessimism • Risk case: • P(red)=P(blue)=.5 • Ambiguous case • w(red)=w(blue) but don’t add to 1 • 1-w(red)-w(blue) is “reserved belief” • …a “vigilance” signal expressed by limbic system? • Bet on red is valued • w(red)u($10)= P(red)u($10) - [P(red)-w(red)]u($10) • risky part pessimism •  look for neural dissociation • Measure strength of ambiguity aversion by w(red)=P(red)γ • γ>1 ambiguity-aversion, γ=1 neutrality γ • Logit “softmax” model P(bet red>x)=1/(1+exp[λ*[xρ-10ρP(red)γ]])

Description-dependent “framing” (descriptions guide attention) • Analogy to figure-ground in perception • Actual study with n=792 docs (Harvard Med, Brigham &Women’s, Hebrew U; McNeil et al JAMA ’80s) • treatment 1 yr 5 yrs choice • Surgery 10% 32% 66% 53% • Radiation 0% 23% 78% 47% • treatment 1 yr 5 yrs choice both frames • Surgery 90% 68% 34% 82% 60% • Radiation 100% 77% 22% 18% 40% • Asian disease problem (-200 vs (1/3) of -600 / +400 vs (2/3) 600 • Pro-choice vs pro-life • Politics: “spin” (Lakoff) • e.g. aren’t we better off w/ Hussein gone? • Liberation vs. occupation • …other examples? • Supply-side response: Competitive framing; which frame “wins”?

Some new frontiers • Animal model • Animals exhibit all EU violations humans do • Field studies • Imagined vs. learned probabilities (Erev, Weber et al Psych Sci) • Emotion and nonlinear w(p) (Hsee-Rottenstreich Psych Sci) • Neural foundations

Prospect theory, I • Key features: • Reference-dependence, nonlinear w(p) • Reference-dependence • Extension of psychophysics (e.g. hot-cold) • U(x-r) • U(.) “reflects” (gamble over losses) • Loss-aversion • Q: Is loss-aversion a preference or a forecasting mistakes (underestimates emotional “immunity” a la Tim Wilson-Dan Gilbert)?

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

Reference-dependence modelling(Koszegi-Rabin, 05) • Two problems in prospect theory: • Is v(c-r) the only carrier of utility? Probably not… • How is r “chosen”? Perceptual? Expectations? How are expectations chosen? • KR solution • U(c|r)= m(c)+µ(m(c)-m(r)) separable into consumption and “surprise” utility • For distributions F, F*=argmaxF∫cu(c|r)dF(c) • For reference distribution G, F*=argmaxF∫c∫ru(c|r)dF(c)dG(r) • Axioms: • A0: µ(x) continuous, twice differentiable (for x≠0), µ(0)=0 • A1: µ(x) strictly increasing (µ’(x)>0) • A2: If y>x>0, then µ(y)+µ(-y)<µ(x)+µ(-x) • (convexity of disutility is weaker than concavity of utility) • A3: µ’’(x)≤0 for x>0 and µ’’(x)≥0 for x<0 (reflection effect) • A3’: For all x≠0, µ’’(x)=0 (piecewise linear utility) • A4: limx-->0µ’(-|x|) / limx-->0µ’(|x|) = λ > 1 (coef. of loss-aversion)

(a,b,c) means display a, then pay b or c One: stochastic dominance Two: reference-dependence (risky) Three: reference-dependence (riskless) Monkey loss-aversion

Reference-dependence • Sensations depend on reference points r • E.g. put two hands in separate hot and cold water, then in one large warm bath • Hot hand feels colder and the cold hand feels hotter • Loss-aversion ≡ -v(-x) > v(x) for x>0 (KT 79) • Or v’(x)|+ < v’(x) |- …a “kink” at 0; “first-order risk-aversion” aka focussing illusion? • Requires theory of “mental accounting” • What gains/losses are grouped together? • When are mental accounts closed/opened? • Conjecture: time, space, cognitive boundaries matter • Example: Last-race-of-the-day effect (bets switch to longshots to “break even”, McGlothlin 1956)

Reference-dependence modelling(Koszegi-Rabin, 05) • Prop 1: If µ satisfies A0-A4, then “reference point preference” follows • (If A3’), then for F and F’, U(F|F’) ≥U(F’|F’)  U(F|F) ≥U(F’|F) • Big move: What is reference distribution? • Impose “personal equilibrium”: r=F* • Pro: Ties reference point to expected actions • Con: If µ(x) is a “prediction error” designed for learning, r=F* means there is nothing to learn • Implication: Can get multiple equilibria (buy if you plan to buy, don’t buy if you don’t) • Role for framing/advertising etc. in choosing an equilibrium (supply side response)

Endowment effects (KKT JPE ’90)

KKT “mugs” experiment (JPE ‘90)

Reference-dependence and endowment effects • Koszegi-Rabin applied to pens (xp), $ (xd) • Utility is direct plus “transition utility” t(.) • ω is weight on ref-dependent utility, λ is strength of loss-aversion

Endowment effects analysis • Choosing (choice-equivalent Pc) • Reference points r(p)=r(d)=0 • U(gain pen)=b+ωb U(gain Pc)= Pc+ ωPc • Equating gives Pc=b • Selling (selling price Ps) • Reference points r(p)=b, r(d)=0 • U(“lose” pen, gain $) • U(keep pen, gain 0)= b • Equating gives Ps= • Buying price Pb = • Prices ordered by Ps>Pc >Pb iff λ, ω>0

Plott-Zeiler review

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

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

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

Disposition effects in housing (Genesove and Mayer, 2001) • Why is housing important? • It's big: • Residential real estate $ value is close to stock market value. • It’s likely that limited rationality persists • most people buy houses rarely (don't learn from experience). • Very emotional ("I fell in love with that house"). • House purchases are "big, rare" decisions -- mating, kids, education, jobs • Advice market may not correct errors • buyer and seller agents typically paid a fixed % of $ price (Steve Levitt study shows agents sell their own houses more slowly and get more $). • Claim: • People hate selling their houses at a "loss" from nominal [not inflation-adjusted!] original purchase price.

Boston condo slump in nominal prices

G-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.

“Constructed” preferences SS200 Colin Camerer