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312 Decisions involving groups of individuals
model which was too complex to be useful. Two methods of combining
individual estimates of unknown quantities are considered below.
Taking a simple average of the individual judgments
First, let us examine the situation where the individual group judgments
can be regarded as being unbiased (i.e. there is no tendency to overor
underestimate), with each person’s estimate being equal to the true
value plus a random error which is independent of the errors of the
other estimates. In these circumstances it can be shown that taking the
simple average of the individual estimates is the best way of aggregating
the judgments. The reliability of this group average will improve as
the group size increases because the random error inherent in each
judgment will be ‘averaged out’. However, each additional member of
the group will bring progressively smaller improvements in reliability,
so that a point will be reached where it will not be worth the effort or
cost of extending the group because a sufficiently reliable estimate can
be achieved with the existing membership.
The situation described above is rarely encountered in practice. Generally,
the members of the group will produce estimates which are
positively correlated. For example, if one member has overestimated
next year’s sales there will be a tendency for the other members to do
likewise. This is likely to occur because group members often have similar
areas of expertise or because they all work in the same environment
where they are exposed to the same sources of information. If there is
a high intercorrelation between the judgments of the group members,
then little new information will be added by each additional member
of the group and there may be little point in averaging the judgments
of more than a small group of individuals. For example, Ashton and
Ashton 2 conducted a study in which a group of 13 advertising personnel
at Time magazine were asked to produce forecasts of the number of
advertising pages that would be sold by the magazine annually. When
the simple average of individuals’ forecasts was used, it was found that
there was little to be gained in accuracy from averaging the forecasts of
more than five individuals.
Taking a weighted average of the individual judgments
When some members of the group are considered to be better judges than
others then it may be worth attaching a higher weight to their estimates
and using a weighted average to represent the group judgment. For