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Aggregating preference judgments 315
leads to an improvement in performance over simple averaging (see, for
example, Winkler 7 and Seaver 8 as cited in Ferrell 1 ).
What are the practical implications of this discussion? The most
pragmatic approach to aggregating probabilities would appear to be the
most straightforward, namely, to take a simple average of individual
probabilities. This method may not be ideal, as our example of the civil
engineering project showed, but as von Winterfeldt and Edwards 9 put
it: ‘The odds seem excellent that, if you do anything more complex, you
will simply be wasting your effort.’
Aggregating preference judgments
When a group of individuals have to choose between a number of
alternative courses of action is it possible, or indeed meaningful, to
mathematically aggregate their preferences to identify the option which
is preferred by the group? To try to answer this we will first consider
decision problems where the group members state their preferences for
the alternatives in terms of simple orderings (e.g. ‘I prefer A to B and B to
C’). Then we will consider situations where a value or a utility function
has been elicited from each individual.
Aggregating preference orderings
One obvious way of aggregating individual preferences is to use a simple
voting system. However, this can result in paradoxical results, as the
following example shows.
Three members of a committee, Messrs Edwards, Fletcher and Green,
have to agree on the location of a new office. Three locations, A, B and C,
are available and the members’ preference orderings are shown below
(note that > means ‘is preferred to’):
Member Preference ordering
Edwards A > B > C
Fletcher B > C > A
Green C > A > B
If we now ask the members to compare A and B, A will get two votes
and B only one. This implies: A > B. If we then compare B and C, B will