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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Economic Review, 73, 596-605.Slovic, P., Griffin, D., & Tversky, A. (1990). Compatibility effects in judgment and choice. In R.
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