Thinking and Deciding

THE MEASUREMENT OF UTILITY 327
Time tradeoff and person tradeoff
We can compare the utility of outcomes by using duration or number of people,
instead of probability, to modify the utility of one outcome so that it becomes equal
to another. Suppose we want to assess your judged utility of curing a persistent
but not very serious cough, compared to that of curing persistent and excruciating
headaches. We can describe each to you in some detail. Then we ask, “How many
days of headaches is just as bad as ten days of cough?” If you say two, we can
conclude that the headaches, as described, are five times as bad as the cough. We
infer this by assuming that duration multiplies the utility per day. You are thus telling
us that two times the daily disutility of headache equals ten times the daily disutility
of cough, in your judgment. This method of utility assessment is called the timetradeoff.
We could use this method to evaluate chest pain of the sort described in the
section on standard gambles. We could ask, “Imagine you have a choice of living
ten years with chest pain or some shorter period T in normal health. You die at the
end. What is T so that you are indifferent?” An answer of seven years implies a
willingness to sacrifice duration of life for quality. Again, we assume that the total
utility of some condition, compared to death as 0, is constant over time, so that we
can add up the utilities year by year (or day by day). This amounts to multiplying the
utility per year by the duration in years. In this case 7 · U(normal) =10· U(pain).
If the utility of normal health is 1, then the utility of pain is .70.
Notice that we left death out of the last equation. We can do that because it has a
utility of 0. The full equation would be 7·U(normal)+3·U(death) =10·U(pain).
In other words, seven years of normal health followed by three years of death is just
as bad as ten years of pain. Putting it this way calls attention to a strange feature
of using death to anchor one end of the scale, as usually done when eliciting health
utilities. We assume that the states of interest exist over time, and we multiply the
duration of a state by its utility per unit time to get the total utility. But death is not
exactly a state. It is more like an event. The badness of being dead does not so clearly
accumulate as a result of being dead for a longer time. On the other hand, the reasons
that we have to avoid death are much the same reasons that we have for wanting to
live, and many of these involve what we can do with our lives — including both
accomplishment and enjoyment. Poor health is bad because it limits what we can do
and how good we can feel, so life in poor health is truly not as valuable as life in
good health. We can do the same amount in a shorter period with good health as we
can in a longer period of poor health. The time-tradeoff method, used with death at
the end, is a way of asking people to make this judgment very explicitly.
Empirically, judgments made this way do not conform to the assumption that
the utility of health is constant over time. When durations are very short, many
people give absolute priority to living as long as possible (Miyamoto and Eraker,
1988). They will say, for example, that ten weeks in pain (followed by death) is
equivalent to ten weeks in normal health (followed by death), but if the units are
changed to years, rather than weeks, they might say that seven years in normal health