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314 Decisions involving groups of individuals
In the absence of these conditions a simple average of individuals’
judgments will probably suffice.
Aggregating probability judgments
There are particular problems involved when probabilities need to
be aggregated, as the following example shows. The managers of a
construction company need to determine the probability that a civil
engineering project will be held up by both geological problems and
delays in the supply of equipment (the problems are considered to
be independent). Two members of the management team are asked to
estimate the probabilities and the results are shown in Table 12.4. It can
be seen that the ‘group’ assessment of the probability that both events
will occur differs, depending on how the averaging was carried out.
If we multiply each manager’s probabilities together and then take an
average we arrive at a probability of 0.24. However, if we first average
the managers’ probabilities for the individual events and then multiply
these averages together we obtain a probability of 0.225.
Because of these types of problem a number of alternative procedures
have been suggested for aggregating probabilities. One approach is
to regard one group member’s probability estimate as information
which may cause another member to revise his or her estimate using
Bayes’ theorem. Some of the methods based on this approach (e.g.
Morris 5 and Bordley 6 ) also require an assessment to be made of each
individual’s expertise and all are substantially more complicated than
simple averaging.
Another approach is to take a weighted average of individual probabilities,
using one of the three methods of weighting which we referred to
earlier. However, again there appears to be little evidence that weighting
Table 12.4 – Averaging probabilities
p(geological
problems)
p(equipment
problems) p(both)
Manager 1’s estimates 0.2 0.6 0.2×0.6 = 0.12
Manager 2’s estimates 0.4 0.9 0.4×0.9 = 0.36
Average = 0.24 But:
Average of the estimates 0.3 0.75 0.3×0.75 = 0.225