Preferences Reversal

Violation of procedure invariance

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.

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.

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.

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.

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.

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.

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).

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 $.

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.

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

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)

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.

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.

Standard

• Procedure invariance and transitivity hold:

CH ~ H > L ~ CL < CH

• Transitive preferences.

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)

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

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).

Illustration

Diagnosis

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).

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).

Experiment on the highway safety program

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.

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.

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.

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.

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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

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