Thinking and Deciding

THE MEASUREMENT OF UTILITY 333
between a motorcycle and a tank. You could do this again, using another dimension
as the standard, in order to check your consistency. If you think the price difference
is .8 of the safety difference and the environmental difference is .2 of the safety
difference, then you should think that the environmental difference is .25 of the price
difference.
You could use these weights to convert the utility of one scale into the units of
another. For example, suppose you assigned 100 “price-utility points” to the difference
between $0 and $40,000, so that $0 had 100 points and $40,000 had 0. And you
assigned 100 safety-utility points to a tank and 0 to a motorcycle. But now you want
to decide between:
A. A car that has 50 price-utility points (because you think that is the
right number for $20,000, its cost) and 60 safety-utility points (because
it is a bit closer to a tank than a motorcycle) and,
B. A car that has 31 price-utility points (instead of 50) and 80 safetyutility
points (instead of 60).
If you just look at the points, you would choose car B, because the total is higher
(31 + 80 versus 50 + 60). But the price points aren’t worth as much. So you convert
the price points into safety points. You know that 100 price points is the same as 80
safety points. That was your judgment. So each price point is worth .8 safety points.
To convert everything to safety points, you multiply the safety points by .8 before
you add. Then car A is better, because it is 50 + 48 safety points instead of 31 + 64.
It doesn’t matter which scale we use, since utility has no particular unit. We just have
to use the same scale for everything.
The next chapter will provide another example of this later, in discussing multiattribute
utility theory. In that theory, the relative difference is called a “weight.”
It is very important to notice here what we are not asking. We are not asking
“How important is recovery time relative to money?” (or price relative to safety).
That question has no meaningful answer. The answer depends on how much money
and how much time. The utility difference between 2 and 3 days recovery time
is smaller than that between $0 and $100 but larger than that between $0 and $5.
This point is not widely understood. People who make up attitude questionnaires —
professionals as well as amateurs (such as politicians) — often ask such questions as
“Which is more important to you, controlling crime or protecting the environment?”
Or they ask you to rate several issues for “importance.” The right answer is, “It
depends on how much of each you are talking about. Preventing a single mugging
is not as important as eliminating all cases of pollution-caused illness, but reducing
crime by 50% is more important than eliminating pollution from a single stream.”
The problem here is related to the prominence effect discussed in Chapter 12.
People seem to have a concept of “importance” that does not depend on quantities.
This is what influences choice in the prominence effect. It is also what allows people
to answer questionnaires that ask about importance but do not specify quantity. It
is not clear what importance means. In particular, it is not clear how we use importance
judgments to make concrete decisions, which involve quantities. If we are