Thinking and Deciding

326 UTILITY MEASUREMENT
Of course this method of measuring utility is valid only if Bernoulli’s assumption
that people choose gambles according to their expected utility is correct. In fact, we
do not always choose in this way (Chapter 11). For example, people may prefer a
gamble (such as a Down syndrome child with probability p and a normal child with
probability 1 − p) to a quite certain outcome (such as a miscarriage with probability
1), even though the gamble would have the same “true” expected utility (see Chapter
11). The knowledge that a particular bad outcome is certain to occur apparently
interferes with making decisions consistent with expected-utility theory; the hope of
avoiding any bad outcome seems to take control.
More generally, the π function of prospect theory (Chapter 11) implies that judgments
made in this way will be inaccurate and inconsistent with each other. Such
inconsistency happens (de Neufville and Delquié, 1988). For example, a subject is
indifferent between $70 with probability 1 and $100 with probability .5, so the utility
of $70 is .5 (if $100 has utility 1). But the utility of the $70 is inflated by the π
function. Suppose we cut both the probabilities in half. The subject now says that
a .25 chance of $100 is equivalent to a .5 chance of $60, not $70. The same subject
might say that a .125 chance of $100 is equivalent to a .25 chance of $55. The
$70, $60, and $55 would be the same if the subject followed expected-utility, but this
sort of difference is typical. The inconsistency gets smaller (in terms of ratios) as
probabilities are reduced, but it does not go away.
Another problem is that different utility estimates result from asking people to
fill in the probability than from asking them to fill in the value of the certain option
(Hershey and Schoemaker, 1986). Suppose you ask, “What probability of $100 is
just as good as $50 for sure?,” and the subject says .7. Then you ask, “What amount
of money is just as good as a .7 chance of $100?,” and the same subject says $60.
Several psychological factors are at work in explaining this discrepancy (Schoemaker
and Hershey, 1992). One effect (but not the only one) is that, when subjects are
given a choice with probability 1, they regard that as the reference point, so that they
demand a higher chance of winning to compensate for the fact that they might “lose
” (for example, the .7 probability just described). They are less likely to do this when
they must name the amount of money, so they are not so risk averse (as in the $60
response — a risk-neutral subject would say $70).
In sum, the use of standard gambles to infer utility is seriously flawed. No way
has been found of compensating for these flaws. The method may still be useful
when we need only a rough answer, and this is often all we need. For example, the
amniocentesis decision, for most couples, is not close at all. One option has several
times the utility of another, depending on the couple’s utility for avoiding Down
syndrome, miscarriage, and abortion. The method is difficult to use, though, and,
if all we need is a rough estimate, direct rating might be quicker and easier, or the
difference method, if we can use it.