Violations of the Expected Utility Hypothesis

Violations of the Expected Utility Hypothesis
Although the expected utility model is sometimes viewed as being quite flexible (since the von Neumann-Morgenstern utility function could have any shape), it does generate refutable predictions. Unfortunately,
there is a growing body of evidence to suggest that individuals’ preferences over lotteries tend to systematically violate some of these predictions. Risk preferences tend to systematically depart from the expected utility property of linearity in the probabilities. The most
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24 Machina
notable example of this is the well-known Allais Paradox (Allais 1953), which asks individuals to rank each of the following pairs of lotteries
(where $1M denotes $1,000,000):
0.10
chance of $5M
0.89
chance of $1M
0.01 chance of $0
 
{ 1.00 chance of $1M
:
:
a1
versus a
2
0.10
chance of $5M
0.11 chance of $1M


:
:


a
versus a
4
0.90
chance of $0
0.89 chance of $0


Experiments by Allais and others have found that the modal (and in some studies, the majority) choices are for a1 over a2 in the first pair, and a3 over a4 in the second pair. However, a preference for a1 in the first pair implies that the utility function satisfies the inequality 0.11⋅U($1M) > 0.10⋅U($5M) + 0.01⋅U($0), whereas a preference for a3 in the second pair implies 0.11⋅U($1M) < 0.10⋅U($5M) + 0.01⋅U($0), which is a contradiction.
Although the Allais Paradox was originally dismissed as an isolated
example, subsequent work by MacCrimmon and Larsson (1979), Kahneman and Tversky (1979), and others have uncovered a qualitatively
similar pattern of departure from the expected utility hypothesis of linearity in the probabilities, over a large range of probability and payoff values (see Machina 1983, 1987 for surveys of this evidence).