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 selfcorrect 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
preferences.
elicitation
might
affect
our
• 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 $.
Relevance of subjective perception
•
Gambles are compounded by several
attributes
whose
saliency
is
determined by the specific frame of
the decision problem.
•
Restrictions on this many-one
relationship are to be found in the
cognitive process of information
processing.
•
Choosing and pricing tasks are
logically equivalent but are perceived
differently because of the different
weigh of their attributes: probabilities
and payoffs.
•
Information processing is causally
relevant in preferences elicitation.
•
If preferences are systematically
responsive to different elicitation
methods, then they violate procedure
invariance.
•
If logical analysis postulates a one-toone
correspondence
between
individuals’ cognition and the
structure of the choice problem, the
relevance of individual perception
postulates a many-one relation.
Formal structure of preferences
reversal
• Let H be the high probability gamble (P bet) and L the
low probability one ($ 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).
•
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
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
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
normatively irrelevant stimuli.
responsive
to
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.
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, 129138.
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.