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How useful is utility in practice? 121
Figure 5.15 – Allais’s paradox
A
B
X
Y
(a)
(b)
$1 million
0.89
0.10
0.01
0.9
0.1
0.89
0.11
$1 million
$5 million
$0
$0
$5 million
$0
$1 million
Another criticism of utility relates to what is known as Allais’s paradox.
To illustrate this, suppose that you were offered the choice of options A
and B as shown in Figure 5.15(a). Which would you choose? Experiments
suggest that most people would choose A (e.g. see Slovic and Tversky 13 ).
After all, $1 million for certain is extremely attractive while option B
offers only a small probability of $5 million and a chance of receiving $0.
Now consider the two options X and Y which are shown in Figure
5.15(b). Which of these would you choose? The most popular choice in
experiments is X. With both X and Y, the chances of winning are almost
the same, so it would seem to make sense to go for the option offering
the biggest prize.
However, if you did choose options A and X your judgments are in
conflict with utility theory, as we will now show. If we let u($5 m) = 1
and u($0) = 0, then selecting option A suggests that:
u($1 m) is greater than 0.89 u($1 m) + 0.1 u($5 m) + 0.01 u($0 m)
i.e. u($1 m) exceeds 0.89 u($1 m) + 0.1 which implies:
u($1 m) exceeds 0.1/0.11