Logical Decisions - Classweb

Figure 9-8 shows how a tradeoff can be used to compute the
relative importance of two measures. In box 1, the decision maker
is asked to choose which alternative is preferred: a car having 110
hp and costing $7,000 or a car having 180 hp and costing $12,000.
In box 2, the decision maker replies that she prefers the two
alternatives equally.
Since she prefers the alternatives equally, they should have equal
utilities. Since a MUF is (usually) a weighted average of the
utilities of the active members, this means that the two weighted
averages must be equal. When comparing the weighted average
for the two simplified alternatives, we see that the terms for the
members other than the ones in the tradeoff drop out. This is
because the levels on all members not explicitly mentioned in the
tradeoff are assumed to be equal.
Thus, the weight for horsepower times the utility for horsepower
plus the weight for cost times the utility for cost must be equal for
the two alternatives in the tradeoff. This implies in turn that the
change in utility for horsepower times the weight for horsepower
must equal the change in utility for cost times the weight for cost.
The two changes must just compensate for each other in order for
the alternatives to have equal overall utilities. This is shown in
box 3. In box 4, we use the previously assessed SUFs to identify
the change in utility for horsepower and cost for the two
alternatives.
In box 5, we see that the change in utility for horsepower is only
half the change for cost. Thus, the weight for horsepower must be
twice the weight for cost. The mathematics of this process are
described in the Appendix on page A-1.
Establishing Tradeoffs. All of the computations needed to
convert tradeoffs to relative weights are done automatically by
LDW. The only thing the decision maker has to do is establish the
tradeoff pairs of equally preferred alternatives.
Typically, tradeoffs are assessed with the help of a graph that has
one member on the horizontal axis and of the other on the vertical
axis. Each point on the graph represents a possible alternative.
These simplified alternatives are assumed to have identical levels
on all of the other evaluation measures and goals.
In the tradeoff assessment process, LDW highlights two points on
the graph and asks the decision maker which she prefers. Based
9-44 Section 9 -- In Depth