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Violation of Utility Theory in Unique and Repeated Gambles

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Gideon Keren
Gideon Keren
Gideon Keren
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Willem A. Wagenaar
Willem A. Wagenaar
Willem A. Wagenaar
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Abstract

This article is concerned with a recent debate on the generality of utility theory. It has been argued by Lopes (1981) that decisions regarding preferences between gambles are different for unique and repeated gambles. The present article provides empirical support for the need to distinguish between these two. It is proposed that violations of utility theory obtained under unique conditions (e.g., Kahneman & Tversky, 1979), cannot necessarily be generalized to repeated conditions. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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Journal of Experimental Psychology:
Learning, Memory, and Cognition
I9S7,
Vol. 13, No. 3, 387-391
Copyright 1987 by the American Psychological Association, Inc.
027H-7.19.V87/SOO.75
Violation of Utility Theory in Unique and Repeated Gambles
Gideon Keren
Institute for Perception, TNO, Soesterberg, The NetherlandsWillem
A.
Wagenaar
State University at Leiden, The Netherlands
This article is concerned with a recent debate on the generality of utility theory. It has been argued
by Lopes
(198
i) that decisions regarding preferences between gambles are different for unique and
repeated
gambles.
The present article provides empirical support for
the need to
distinguish between
these two. It is proposed that violations of utility theory obtained under unique conditions (e.g.,
Kahneman
&
Tversky,
1979),
cannot necessarily
be
generalized to repeated conditions.
In two earlier articles published in this journal, Lopes (1981)
and Tversky and Bar-Hillel (1983) raised an old problem con-
cerning the rationale of expected utility theory. The problem
raised
by
Lopes concerns the distinction between the interpreta-
tion of expected utility (or expected value) in long-run versus
short-run situations. Whereas Lopes accepted utility theory in
long-run situations, she questioned its rationality and applica-
bility to short-run circumstances and unique events. She pro-
posed that "for short-run situations, it is reasonable to consider
the probability of coming out ahead (which is related to the
median outcome of
the
gamble) instead of, or at least in addi-
tion to, the long-run expectation"
(p.
377).
To
support her con-
jecture, she discussed three examples involving unique and re-
peated gambles and concluded that the standard conception of
rational choice, based on the maximization of expected utility,
"is simply not sensible." Tversky and Bar-Hillel have rebutted
Lopes' arguments, mainly by proposing a different analysis of
the examples used by Lopes.
The disagreement between Lopes (1981) and Tversky and
Bar-Hillel (1983) stems, to a great extent, from treating the
problematic issues from different viewpoints and with different
underlying assumptions. As noted by Schoemaker (1982), it is
inappropriate to assess the acceptability of an optimal model
(such as expected utility) without explicit prior statement of
its purpose and underlying assumptions. More specifically, we
suggest that Lopes has pointed out some inadequacies of utility
theory mainly from a
descriptive
point of
view.
In contrast, the
treatment offered by Tversky and Bar-Hillel is more formal and
stems from a
normative
viewpoint.
The goal of the present article is not to expand on the norma-
tive question of whether people should treat unique and re-
peated gambles in the same manner. For the development of
a
psychological theory, it is more relevant to determine whether
in practice people do react differently or in the same manner to
unique and repeated gambles.
Modern utility theory, as developed by Von Neuman and
Morgenstern (1947), claimed not only to provide sound justifi-
We would like to thank Baruch
Fischhoff,
Sarah Lichtenstein,
Charles
Lewis,
and
Charles Vlek
for many valuable comments on previ-
ous drafts of this article.
Correspondence concerning this article should be addressed to Gid-
eon Keren, Institute for Perception,
TNO,
Kampweg 5,3769,
DE
Soest-
erberg, The Netherlands.
cation for the Bernoullian expected utility principle, but also
to show that "this justification does not depend on long run
considerations, hence it is applicable to unique choice situa-
tions"
(Coombs, Dawes,
&
Tversky, 1970, p.
126;
sec also Luce
& Raiffa, 1957). It is therefore not surprising that most investi-
gators did not hesitate to study the application of utility theory
as a model of human decision making by using research para-
digms that contained unique gambles only. This held also for
those who were critical of utility theory, like Allais (1953). A
more recent example is the classical set of experiments pre-
sented by Kahneman and Tversky (1979) to demonstrate the
inadequacy of utility theory. Out of 14 decision problems used
by these investigators, 13 contained unique gambles and the
remaining one (Problem 9) was ambiguous.1 The conclusion
reached by Kahneman and Tversky that "utility theory, as it is
commonly interpreted and applied, is not an adequate descrip-
tive model"
(p.
263), is not necessarily true for decision makers
faced with repeated gambles.
Utility theory treats the two domains, unique and repeated
events, monolkhically. Consequently, most researchers as-
sumed, at least implicitly, that demonstrated violations of util-
ity theory obtained under unique conditions (like those re-
ported by Kahneman & Tversky* 1979) can be generalized to
repeated conditions. The major purpose of the present investi-
gation was to test whether such a generalization is justified.
More specifically, in the experiments reported here, we studied
two robust effects that were used by Kahneman and Tversky to
demonstrate the inadequacy of utility theory in unique cases.
These are the
certainty effect
and
the possibility
effect.
The pur-
pose of
these
experiments
was
to test whether utility theory will
also be violated under repeated (gambles) conditions.
Two of the few researchers to realize the potential difference
between unique and repeated gambles were Coombs and
Bowen (1971), They asked their subjects to rank order different
sets of gambles in terms of their perceived riskiness. A major
variable manipulated by these investigators was the number of
1 Problem 9 offers a probabilistic insurance of property against dam-
age.
Although the decision to insure is taken only once, the damage
(such as
fire
or theft) can occur many times in the period covered by the
contract. Paying half of the premium for coverage on odd days of the
month may be normatively attractive when damage can occur only
once,
ft is very unattractive if damage occurs 10 times, because the
probability that all instances will occur on odd days (the days on which
the insurance is
valid) is
very small.
387
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