Preferences Reversal

1. Preferences Reversal Violation of procedure invariance

2. Wrap up of the previous lecture • Two hypotheses competing for the behavioral foundation of economic theory: DPH, according to which preferences are stable and PCH, according to which preferences change. • Methodological implications. DPH: economic theory performs well only in simple, incentive compatible repeated interactions; PCH: economic analysis might be applied to a wider range of phenomena. • Epistemological implications. DPH: economics is a separate science; PCH: economics develops at the interface with cognitive sciences.

3. Introduction • Decision theory as a topic of mathematics and philosophy: common assumption of stable preferences. • Psychological analysis of decision making starting from the fifties of the XX cent. (Edwards 1954). • Psychological explanations put in question the assumption of stable preferences.

4. Procedure invariance • When a theoretical system postulates an existing entity, the alternative ways to measure it should not produce different results. • The preferences relation should not be affected by different elicitation methods. • Procedure invariance is a necessary condition for utility maximization: without stability across description and logically equivalent elicitation methods one’s preferences cannot be represented as utility maximizing.

5. Example • Consider two tasks: choosing between two lotteries and pricing the same lotteries. • Pricing and choosing are two logically equivalent methods of eliciting the subjective evaluations of the lotteries. • If procedure invariance holds then pricing and choosing tasks reveal the same subjective evaluation.

6. Implications for RCT • The logical structure of the choice problem is independent of individual cognition. • Rational preferences depend on the logical structure and not on cognition. • Rational choices always reveal an independent structure of well ordered preferences. • Individuals might commit mistakes in perceiving differently two logically equivalent problems. • According to the assumption of procedure invariance, if we allow learning, individuals will self-correct these cognitive biases. • In the long run choices reveal a stable structure of preferences: procedure invariance is coherent with DPH.

7. Simon’s model of bounded rationality • Rationality is not independent from the subjective perception of the decision problem: rationality is a product of thought (Simon 1956). • Individuals’ preferences derive from the cognitive mechanism of information processing. • The causal explanation of choice behavior should take into account individuals cognitive limits. • We learn by experience to implement satisfactory – not necessarily maximal - choices. • This learning process shapes our preferences. • Bounded rationality endorses PCH.

8. Operational hypothesis • Preferences construction is a contingent form of information processing. • Methods of elicitation might affect our preferences. • Choosing and pricing tasks might induce systematic reversals of preferences (Slovic & Lichtenstein 1968, 1971, Slovic 1995, Lichtenstein & Slovic 2006).

9. Definition and evidence of preferences reversal • Subjects confront two bets: a $ bet with a low probability to win a large prize and a P bet with a high probability to win a small prize. P bet: 11/12 chance to win 12 chips; 1/12 chance to lose 24 chips; $ bet: 2/12 chance to win 79 chips; 10/12 chance to lose 5 chips • Subject have to make straight choices among the bets and report their WTA valuations for each bet. • The two bets are chosen equally often but this does not mean indifference because 88% of the time $ is priced more highly than P and when subjects choose P, 87% of the time give a higher price to $.

10. Relevance of subjective perception • Gambles are compounded by several attributes whose saliency is determined by the specific frame of the decision problem. • Choosing and pricing tasks are logically equivalent but are perceived differently because of the different weigh of their attributes: probabilities and payoffs. • If logical analysis postulates a one-to-one correspondence between individuals’ cognition and the structure of the choice problem, the relevance of individual perception postulates a many-one relation. • Restrictions on this many-one relationship are to be found in the cognitive process of information processing. • Information processing is causally relevant in preferences elicitation. • If preferences are systematically responsive to different elicitation methods, then they violate procedure invariance.

11. Formal structure of preferences reversal • Let H be the high probability gamble (P bet) and L the low probability one ($ bet). Let CH and CL the cash equivalent of low and high bet. • Normative benchmark (risk aversion is assumed): H ≥ L ˅ CH > CL • Standard pattern of preferences reversal: H ≥ L ˅ CL > CH

12. Procedure invariance in concrete • The assumption of procedure invariance implies an indifference relation between the bets and their cash equivalents. • CH ~ H • CL ~ L • Procedure invariance is violated when the indifference relation is substituted for inequalities. • CH < H (underpricing) • CL > L (overpricing)

13. Intransitivity or violation of procedure invariance • Preferences reversal might be due to the violation of transitivity axiom while procedure invariance holds. In this case we cannot exclude the existence of a stable preferences structure. • Preferences reversal might be due to the violation of procedure invariance while transitivity holds. In this case the existence of a stable preferences structure is questioned.

14. Violation of transitivity • Procedure invariance holds: CH ~ H > L ~ CL > CH • The two inequalities follow from preferences reversal while the two equivalences follow from procedure invariance • Intransitive preferences.

15. Standard • Procedure invariance and transitivity hold: CH ~ H > L ~ CL < CH • Transitive preferences.

16. Violation of procedure invariance • Procedure invariance fails due to under-pricing of H or overpricing of L: • CH < H(Underpricing) • H > L (Reversal) • CL > L (Overpricing) • CL > CH(Reversal)

17. Tversky et al.’s experiment (1990) • The experimental design aims at distinguishing between violation of transitivity or procedure invariance through eliciting preferences ordering and not simply actual selling prices. • Extension of the standard experiment by introducing the option of receiving $ X for sure. The decision maker provides three choices (H-L, H-X, L-X) and two price assessments (CH, CL). • Elicitation method: 1) stating the selling price of each bet separately; 2) presentation of ordered pairs of bets; 3) choosing among the two bets (ordinal payoffs scheme). • A random mechanism determines whether it is going to be played the preferred or the higher priced lottery. Subjects know about the mechanism. • Standard pattern of reversal: H > L and CL> X > CH • Intransitivity: L > X and X > H, yielding L > X > H > L • Overpricing of L (OL): X > H and X > L yielding CL > X > L • Underpricing of H (UH): H > X and L > X, yielding H > X > CH. • Both OL and UH: H > X and X > L yielding H > X > CH and CL > X > L

18. Results • Standard rate of reversal: 40-50%. • 10% of intransitive preferences. • 90% of violation of procedure invariance among which 2/3 are due to overpricing of L (CL > L).

19. Illustration

20. Diagnosis

21. Compatibility hypothesis • The weigh of an attribute is enhanced by its compatibility with the response mode (Slovic 1995): pricing is primarily determined by payoffs while choices are influenced by the probability of winning and loosing. • Twofold rationale: 1) if the stimulus scale and the response scale do not match, this increases the cognitive effort and error so as to reduce the impact of the stimulus; 2) the response mode tends to focus attention on the compatible feature of the stimulus. • Experiment with three riskless pairs with monetary payoffs and three riskless pairs of bets with non-monetary payoffs (Slovic et al. 1990). This design determines the decrease of reversal from 41% (monetary bets) to 24% (non monetary bets).

22. Choice, matching and prominence • Binary choice and matching tasks (i.e. cash equivalent, rating scale and so on) disagree in measuring preferences (violation of procedure invariance). • Prominence effect: the more prominent attribute weighs more in choice than in matching (Tversky et al. 1988).

23. Experiment on the highway safety program

24. Treatment • A group of respondents receive the same problem with a missing value of one the programs and they are asked to state a price to make the two programs equally attractive. • It is possible to infer the person’s choice from its pricing. • I.e. if the X program is missing and the respondents state a price less than $55, then we can infer that those respondents would choose Y over X when the cost of X is $55.

25. Results • 67% of the subject choose the X program. • Inference of an inverted choice for Y when X costs 55$: only 4% of the inferred choices favored the X program. • Marked discrepancy from choice and matching tasks.

26. Common feature of the explanatory hypotheses • Preferences construction is a contingent form of information processing. • Information processing diverges from rational decision models as it excludes a one-to-one correspondence between the decision problem and subject's cognition. • Information processing is responsive to normatively irrelevant stimuli.

27. Conclusions • Preferences reversal might be due to the violation of transitivity axiom, procedure invariance or both. • The empirical evidence support an explanation based on the violation of procedure invariance. • Preferences construction is a highly contingent form of information processing.

28. References Edwards, W. (1954). The theory of decision making. Psychological Bulletin, 51,380-417. Lichtenstein, S. and Slovic, P. eds. (2006). The construction of preference. Cambridge University Press, New York. Simon, H. (1956). Rational choice and the structure of the environment. Psychological Review, 63, 129-138. Slovic, P., & Lichtenstein, S. (1968). Relative importance of probabilities and payoffs in risk-taking. Journal of Experimental Psychology Monographs, 78, 1-18. Slovic, P., &. Lichtenstein, S. (1983). Preference reversals: A broader perspective. American Economic Review, 73, 596-605. Slovic, P., Griffin, D., & Tversky, A. (1990). Compatibility effects in judgment and choice. In R. Hogarth (Ed.), Insights in decision making: A tribute to Hillel J. Einhorn (pp. 5-27). Chicago: University of Chicago Press. Slovic, P. (1995) “The construction of preference.” American Psychologist, 50(5), 364–371. Tversky, A., Sattath, S., & Slovic, P. (1988). Contingent weighting in judgment and choice. Psychological Review, 95, 371-384. Tversky, A., Slovic, P., & Kahneman, D. (1990). The causes of preference reversal. American Economic Review, 80, 204-217.