Thinking and Deciding

MAUT AS A TYPE OF DECISION ANALYSIS 351
Suppose you find that the memory scale is equal to the disk-size scale, so that
you are indifferent between a 640K memory with 100-megabyte hard disk and 64K
memory with a 300-megabyte disk. Then the memory scale would also get half as
much weight as the price scale. To compute the total utility of each model, you
would multiply the memory and disk-size utilities by .5 before adding them. This
would yield utilities of 100, 125, 50, and 75 for the four models, respectively. Your
analysis would tell you to choose model B after all.
Notice that when you determine the weight of the scales, you need to know
what the ends of the scales are. Unless you know the ends, you cannot ask yourself
whether the range in memory size is more important than the range in price, or
vice versa, and this is the question that you must answer. If the price range is only
from $1,500 to $1,600, for example, price would not be very important.
Questions about the relative weights of attributes are not like the usual questions
often seen in opinion surveys, which take the form “Which is more important, reducing
crime or reducing air pollution?” Such questions do not tell us how much crime
and how much pollution are involved. If policy makers knew that a reduction from
2,000 to 1,900 robberies per year was just as good as a reduction of pollution from
100% to 90% of the maximum allowable level, they could decide how to allocate
funds so as to do the most good. If they could reduce air pollution from 100% to 90%
for the same cost as reducing robberies from 2,000 to 1,950, they should choose the
former. But we do not know what citizens mean when they say that “crime is more
important.” We need to know the ranges, when we compare attributes, so that we
can translate the units. If the “robbery attribute” ranged from 2,000 to 1,000, and if
someone said that a reduction in pollution from 100% to 90% was 10% of this range,
then we would know how to use that judgment in making decisions. In essence, we
convert these measures to a common scale. If we want to measure with money, we
convert all the different currencies to a common currency using their rates of exchange.
If we want to measure with utility, we must convert to a common scale of
utility, and we must determine these rates of exchange.
The attributes or dimensions in a multiattribute analysis work best if each of them
corresponds to a fundamental goal or objective ( Keeney, 1992). In many analyses,
as discussed earlier, each attribute is decomposed into subattributes. For example,
in an analysis concerning pollution control, “effects on health” can be decomposed
into “causing new cases of chronic lung disease” and “causing temporary coughs
and breathing difficulties.” Each of these subattributes can be further specified or
decomposed; for example, chronic disease can be decomposed into lung cancer, emphysema,
asthma, and other diseases. Note that each subattribute corresponds to a
part of the goal of minimizing harm to health.
for another attribute. For example, suppose that price range matters more to you than the range of disk
size. You could ask yourself, “How much more than $500 would I pay in order to replace a 100-megabyte
disk with a 300-megabyte disk?” Suppose the answer is “$1,000 more,” so that the total cost is $1,500.
You have now found that the scale for disk size should be weighed half as much as the money scale, for
the difference between the two ends of it equals only the difference between $500 and $1,500, a utility
difference of 50 on the price scale.