Thinking and Deciding

THE MEASUREMENT OF UTILITY 325
Figure 13.1: Tree for outcomes and probabilities of amniocentesis decision
the couple be indifferent between the miscarriage and the gamble? Suppose it is
.02. Then we know — again making the usual assumption that the couple chooses
as Bernoulli says they will — that the expected utility of the gamble is the utility
of the miscarriage. The expected utility of the gamble is .02 · 100 + .98 · 0, or2.
Hence, u(M) =2. In the same manner, we can assess the utility for an abortion. For
example, if p for an abortion is .03, then u(A) is 3. We can then replace u(M) and
u(A) with their estimated values to calculate the overall expected utility of the choice
of amniocentesis, and we can compare this to the expected utility of not having
amniocentesis, which, in this case, is .274. In this case, the expected utility of the
test is .005 · 2+(.995 · .00371) · 3+(.995 · .99629) · 0, or about .011. In this case,
the expected disutility of the test is less than that of not having the test, so the couple
should have it.
This example shows how the method of gambles allows us to break down a complex
decision into a set of simpler ones. Of course, each of the “simple” ones could
also be analyzed into more outcomes, each with its own probability. Down syndrome,
for example, has many manifestations, and miscarriages may be harmful to
the mother or less harmful, and have fewer or more numerous implications for future
births. In this example, we have treated such outcomes as miscarriage and abortion
as holistic entities, not to be analyzed further. We could have treated amniocentesis
itself as a holistic outcome and made the decision without analysis at all. (This is
what most people do.)