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Aggregating preference judgments 319
scale are shown below and it can be seen that San Francisco would now
be the group choice.
Destination Person A Person B Average
Rio de Janeiro 40 50 45
San Francisco 16 100 58
Toronto 0 0 0
Is it possible to compare one individual’s strength of preference
with another’s? French 11 examines a number of ways in which such
comparisons could be made in theory and shows that all the methods
are likely to fail in practice. For example, the whole group might agree
unanimously that person 1 prefers P to Q more than person 2 prefers
X to Y. But what would happen in the likely event of this unanimity
not being achieved? Alternatively, we might use money as the common
yardstick for strength of preference. If person A is only prepared to pay
$100 to transfer from his worst to his best holiday destination while
person B is prepared to pay $1500 then can we say that B’s strength of
preference is greater than A’s? If we answer yes to this question then we
must assume that $1 is equally valued by the two people, but what if A is
a pauper and B a millionaire? Clearly, our ‘objective’ scale would lead us
back to the problem of comparing individuals’ strengths of preference!
In the absence of any obvious method for making interpersonal
comparisons of intensity of preference then it seems that our search
for a group value or utility function is futile. Nevertheless, the concepts
of value and utility can still be useful in group decision making. The
derivation of individual values and utilities can help each group member
to clarify his or her personal understanding of the problem and also to
achieve a greater appreciation of the views of other members. Moreover,
a simple average of values and utilities may be useful in providing
a rough initial model of the problem. Sensitivity analysis can then be
used to test the effect of using individual values and utilities. This may
reveal, for example, that certain options are to be preferred to others,
irrespective of which individual’s utility function is used. At the very
least, the process should lead to a more informed discussion and debate.
This reference to group discussion and debate leads us to the next
section, where behavioral aggregation methods are considered. We begin
by looking at the behavioral problems which can occur when a group of
decision makers meet to agree upon a course of action.