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310 Decisions involving groups of individuals
Two simple advantages arise from obtaining group judgments in
decision analysis. First, more information about possible ranges of
utilities and probabilities can be obtained, and it is then possible to
perform sensitivity analysis on these ranges to see if the decision specified
by the analysis is changed by these variations. Second, a group of
people who are involved in such a decision process may become more
committed to implementing the decision which is eventually made. As
we shall see in the section on decision conferencing, this latter advantage
can be a major one.
Mathematical aggregation
Ferrell 1 provides an excellent and comprehensive discussion of mathematical
and other aggregation methods. Much of the following discussion
is based on his review.
There are a number of advantages to be gained by using mathematical
aggregation to combine the judgments of the individual members of
a group. In particular, the methods involved are relatively straightforward.
For example, we might ask each member of a group to estimate
the probability that the sales of a product will exceed 10 000 units next
year and then calculate a simple average of their estimates. This means
that the more complex and time-consuming procedures of behavioral
aggregation are avoided. Moreover, the group members do not have to
meet. Their judgments can be elicited by telephone, post or computer and
therefore the influence of dominant group members is avoided. However,
there can be serious problems with the mathematical approach as
the following, rather contrived, example shows.
Suppose that a production manager and an accountant have to make
a joint decision between investing in a large- or small-volume processor.
The payoff of the processor will depend upon the average level of
sales which will be achieved during its useful life. Table 12.1 shows the
production manager’s subjective probabilities for the sales levels and his
utilities for the different actions and outcomes. It can be seen that the
expected utility of a high-volume processor is 0.4 (i.e. 0.4 × 1 + 0.6 × 0)
while for the low-volume processor it is 0.412 (i.e. 0.4 × 0.1 + 0.6 × 0.62),
so the production manager will just prefer the low-volume processor.
Table 12.2 shows the accountant’s view of the problem. Her expected
utilities are 0.5 for the high-volume processor and 0.51 for the lowvolume
one so she will also favor the low-volume processor. However,
if we now take the average of the probabilities and utilities of the two