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132 Decision making under uncertainty
as being equivalent to a lottery offering only a 0.757 chance of the
best/best outcome.
Further points on multi-attribute utility
The principles which we applied to the two-attribute problem above can
be extended to any number of attributes (see, for example, Bunn 19 who
discusses a problem involving four attributes), though the form of the
multi-attribute utility function becomes more complex as the number
of attributes increases. Models have also been developed which can
handle situations where mutual utility independence does not exist (see
Keeney and Raiffa 16 ), but the complexities of these models have meant
that they have proved to be of little practical value. In any case, as we
mentioned earlier, if mutual utility independence does not exist it is
likely that by redefining the attributes a new set can be found which
does exhibit the required independence (we discussed the analogous
problem in Chapter 3 when looking at multi-attribute value functions).
The approach to multi-attribute utility which we discussed above
clearly requires a major commitment of time and effort from the decision
maker and, since the method lacks the ‘transparency’ of the SMART
procedure, which we met in Chapter 3, a non-mathematical person may
be suspicious of its results. In all models a balance has to be struck
between the accuracy with which the model represents the real problem
and the effort required to formulate the model. If a problem is of major
importance, and if the decision maker is happy to make the necessary
judgments, then what Watson and Buede 20 refer to as the ‘deep soul
searching’ engendered by Keeney and Raiffa’s approach may lead to
valuable insights into the decision problem. In other circumstances,
where the decision maker only requires outline guidance from the
model, a less sophisticated approach based, for example, on values
rather than utilities may suffice. Sensitivity analysis will provide useful
guidance on the robustness of any approximations which are used.
Summary
In this chapter we have considered a number of methods which enable
a decision maker to make rational decisions when the outcomes of
courses of action are not known for certain. The approach based on
expected monetary value was relatively simple, but if the decision