Thinking and Deciding

320 UTILITY MEASUREMENT
Simple direct judgment and the analog scale
The simplest way to estimate utility is to assign numbers to the various outcomes.
For example, suppose you must decide whether to accept a job or to refuse it and
hope for a better offer, which you expect with a probability of .5. There are three
possible outcomes: the job you have been offered (B); the better offer (A); and the
job you would have to take if the better offer does not come through (C). To assess
your expected utility, you might assign a value of 100 to job A, and a value of 0 to
job C, and ask yourself where job B falls on this scale. Clearly, if the value of job
B is greater than 50, the expected utility of accepting job B is higher than that of
waiting.
A visual aid like the following is often used to help subjects make judgments like
this. The ends of the line are labeled with the extreme conditions (A and C), and the
subject is asked to mark the line where the other condition falls (B). This is called
the visual analog scale. We have no evidence that the visual aspect of it helps in any
way, but also no evidence that it hurts.
A B C
The direct approach has the virtue of simplicity, but it has a couple of defects.
First, you (the judge of your utilities) have not been told much about what the numbers
you assign are supposed to mean. The only requirement that is obvious to you
is that higher numbers should correspond to higher utilities. You are free to assign
ratings that express the square of the utility (or some other function) rather than the
true utility. If you did this, a rating of 36 for job B would correspond to a true utility
of 6, and a rating of 100 would correspond to a utility of 10. Although the analysis
would say that you should decline job B (because 36 is less than 50, which is half the
assessed utility of A), the true utilities would say that you should take job B (because
6 is greater than 5, which is half the true utility of job A).
Another problem with direct scaling (and perhaps with other methods) is that
psychological experiments suggest the relative ratings chosen depend on the set of
stimuli used. For example, if subjects are asked to rate the length of rods that are
respectively 1, 3, 5, 7, 8, 9, and 10 inches long, they tend to rate the longer rods
as more different in length and the shorter rods as closer in length than they really
are. If, on the other hand, subjects are given rods with lengths 1, 2, 3, 4, 6, 8,
and 10 inches, the reverse is found (Poulton, 1979). The same may be true for rating
utilities. In general, judgments tend toward even spacing, or equal use of all response
categories (Mellers and Birnbaum, 1982; Parducci, 1965).
These effects might be avoidable by selecting stimuli carefully (on the basis of
preliminary studies) or by presenting only three stimuli at a time. A form of this
effect still happens even with three stimuli, however. Suppose you are asked, “On a
scale where 0 is being blind and deaf and 100 is normal health, where is being blind?”