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Multi-attribute utility 125
Mutual utility independence
Suppose that the project manager is indifferent between the following
alternatives:
A: A project which will certainly overrun by 2 weeks and which will
certainly cost $50 000; and
B: A gamble which will give him a 50% chance of a project which
overruns by 0 weeks (i.e. it meets the target) and which will cost
$50 000 and a 50% chance of a project which will overrun by 6 weeks
and cost $50 000.
These alternatives are shown in Figure 5.17(a) (note that all the costs are
the same).
Suppose that we now offer the project manager the same two
options, but with the project costs increased to $140 000, as shown
in Figure 5.17(b). If the project manager is still indifferent between the
options then clearly his preference between the overrun times is unaffected
by the change in costs. If this is the case for all possible costs then
overrun time is said to be utility independent of project cost. Putting this
in more general terms: attribute A is utility independent of attribute B
if the decision maker’s preferences between gambles involving different
levels of A, but the same level of B, do not depend on the level of
attribute B.
It can be seen that utility independence is analogous to preference
independence, which we discussed in Chapter 3, except that we are now
A:
C:
Figure 5.17
1.0
1.0
Overrun Cost
2 weeks $50000
Overrun Cost
2 weeks
(a)
$140000
(b)
B:
D:
0.5
0.5
0.5
0.5
Overrun Cost
0 weeks $50000
6 weeks $50000
Overrun Cost
0 weeks
$140000
6 weeks $140000