HUMAN BEINGS ARE MORE RATIONAL THAN WE THINK

Transcription

1 HUMAN BEINGS ARE MORE RATIONAL THAN WE THINK David H. Wolpert NASA Ames Research Center NASA-ARC

2 HYPOTHESIS Often humans are rational, but appear irrational to us, the modelers, because we misconstrue their decision problems. If true, then to best predict / control human behavior, whenever they appear to be irrational, we must be careful in modeling their decision problem Income comparison - happiness determined by relative income - appears to be irrational...

3 INCOME COMPARISON Men do not desire to be rich, but richer than other men. - John Stuart Mill Our wants are in relation to society; they are relative. - Karl Marx I do count my blessings. But then I count those of others who have more, and that pisses me off. - New Yorker cartoon WHY?

4 INCOME COMPARISON 1) Experiment: If your neighbor s income is moderately greater than yours, it makes you unhappy. 2) Experiment: If your neighbor s income is much greater than yours, or less than yours, it does not make you unhappy. 3) Such income comparison holds in almost all cultures. (Can be confounding factors though.) 4) Income comparison may even be corroborated by fmri studies. WHY?

5 INCOME COMPARISON 1) Effects of income comparison: People will choose to have lower income, if that means others have even lower income. 2) Effects of income comparison: Beyond a certain minimal level, as countries become richer, their citizens do not become happier. (The Easterlin paradox.) 3) Effects of income comparison: Some economists have argued that government should not try to imize GDP. Rather imize average national happiness. This implies reducing income inequality.

6 ONLY IDEAS IN THIS TALK: 1) Observing others may provide information on how to modify behavior to imize future expected payoff 2) Unhappiness often causes us to modify our behavior Observing others may rationally cause unhappiness 3) Is all unhappiness such a computational shortcut?

7 MODEL OVERVIEW Model the statistical implications of (Payoff of Decision maker D) - (Payoff of Neighbor N) on Change in D s payoff if he searches for a new strategy

8 MODEL CONCLUSIONS 1) If (D s payoff - N s payoff) > 0, the difference does not predict that D s payoff would rise if D searched. Ignore the Bundy s (those with less income) 2) If (D s payoff - N s payoff ) << 0, the difference does not predict that D s payoff would rise if D searched. Ignore the Vanderbilts (those with much greater income) 3) If (D s payoff - N s payoff ) < 0, the difference predicts that D s payoff would rise if D searched. Keep up with the Joneses

9 MODEL IMPLICATIONS 1) Some payoff differences between D and N imply that D should search for a new strategy x. 2) In real world, often if D is unhappy about a payoff difference with N, D searches for a new strategy x; a Hedonic Prod. Example: x is the style D uses to play a sport, payoff is how frequently D wins. Hypothesis: Hedonic prods are a computational shortcut for the full calculation saying D should search, changing D s behavior to make him search

10 MODEL ATTRIBUTES 1) Model may explain data concerning domains other than income 2) Model makes testable predictions - so it s refutable. 3) Model potentially extensible to explain other phenomena: U-shaped lifetime happiness curves hedonic contagion self-handicapping

11 MODEL DETAILS x X possible strategies D and N can adopt f D (x) payoff function of D f N (x) payoff function of N L D set of N D pairs (x, f D (x)) - D adopts the best of those, having payoff L D L N set of N N pairs (x, f N (x)) - N adopts the best of those, having payoff L N

12 MODEL DETAILS Search of f D is IID sampling of y s from window function W σ (µ D, y) = 1/σ if y - µ D σ / 2 = 0 otherwise where σ is known, but mean µ D is not. Same for search of f N, with mean µ N. With probability ρ, µ N = µ D, drawn from h. Otherwise they are independently drawn from h: P(µ N, µ D ) = ρδ(µ N, µ D )h(µ N ) + (1 - ρ)h(µ N )h(µ D )

13 MODEL DETAILS The hedonic prod is posterior expected change in D s payoff if D searches for (and adopts) another x: H(L D, N N, L N ) = E(f D (x) - L D L D, N N, L N ) Search for new x iff H(L D, N N, L N ) > 0 Many simplifications: - Cost-free search - Infinite cost to decline new x and return to L D - Extremely simple statistical model of search - D knows N N (how hard N searched) and L N (N s best payoff), but nothing else about N s search

14 MODEL SUMMARY x X possible strategies D and N can adopt f D (x) payoff function of D f N (x) payoff function of N L D set of N D pairs (x, f D (x)) L N set of N N pairs (x, f N (x)) - D adopts the best of those x s, L D - N adopts the best of those x s, L N µ D, µ N means of payoffs for D and N σ width of payoffs for D and N ρ prior probability that µ D = µ N H the hedonic prod; search iff H > 0

15 MODEL SUMMARY

16 MODEL SUMMARY

17 MODEL SUMMARY

18 MODEL SUMMARY

19 MODEL SUMMARY

20 THE VANDERBILTS AND BUNDYS If L D - L N > σ, or L N - L D min > σ, H = L D min +σ / 2 L D σ / 2 L D min +σ / 2 L D σ / 2 dt th(t) dt h(t) L D This H is independent of all that D knows about N Intuition: D concludes that f N and f D are independent Conclusion: Ignore the Vanderbilts and the Bundys

21 THE VANDERBILTS AND BUNDYS If L D - L N > σ, or L N - L D min > σ, H = L D min +σ / 2 L D σ / 2 L D min +σ / 2 L D σ / 2 dt th(t) dt h(t) L D 1. As N D grows, L D - L min D approaches σ 2. So for fixed L N - L D > 0, as N D grows, L N - L min D grows 3. So for fixed gap in payoffs, the more D has searched, the more likely that he concludes that N is a Vanderbilt

22 THE JONESES For simplicity, let h be a very wide window function. Then if L D - L N > 0, H 0: Everyone with less payoff than you is a Bundy Remaining case: L D < L N L D min + σ If ρ 0, H 0 Intuition: D concludes that f N and f D are independent

23 THE JONESES h a very wide window function, and L D < L N L D min + σ: If ρ substantially non-zero, where: H σ γ N N N N + 1 β = (L N - L D min )/ σ γ = (L N - L D min )/ σ < β 1 β N N β N N

24 THE JONESES h a very wide window function, L D < L N L D min + σ, ρ > 0: H σ γ N N N N β N N β N N 1) Can have H > 0: Intuition: D concludes f N = f D, and that a new sample of f N would likely exceed L D : Keep up with the Joneses. 2) Can have H < 0: Intuition: D concludes f N = f D, but N N is so large that a new sample of f N would likely be less than L D

25 RELATION TO PREVIOUS WORK Herding (information cascades) Tiny search space (e.g., binary) Observe neighbor s move, not just payoff Not been related to hedonic utility Social comparison Typically observe many neighbors, not just one Observe neighbor s move, not just payoff Not been related to hedonic utility Indirect social influence (conformity due to biased sampling) Observe neighbor s move only Not been related to hedonic utility

26 RELATION TO PREVIOUS WORK Cognitive limitations (Friedman, Robson, Netzer, Rayo and Becker) Assumes bounded rationality of one type (e.g., finite number of possible happiness values) to explain another (income comparison) Little (no?) experimental data supporting that assumed bounded rationality. Samuelson s model Very complicated Usual problems of evolutionary psychology Frank s musings (and others) No formal model

27 FUTURE WORK 1) Self-handicapping Generalization of inappropriate prods: D chooses action guaranteeing f N f D, to avoid hedonic prod. Experiment: People may handicap themselves to have excuse ready to explain why they later lose. 2) Hedonic contagion If D know N well enough to know f N = f D, N s (lack of) a prod provides D information about whether D should have a hedonic prod. Experiment: (Un)happiness of someone s close social contacts greatly affects their (un)happiness.

28 CONCLUSION 1) Observing others may provide information on how to modify behavior to imize payoff 2) Unhappiness often causes people to modify behavior 3) Therefore observing may others may rationally cause someone to be unhappy; a hedonic prod 4) This explains much experimental data on income comparison 5) Like other computational shortcuts, a hedonic prod may be inappropriately stimulated. (Agrees with experiment.) Is this the basis for the emotion of unhappiness in all contexts?