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Aggregating preference judgments 317
In his well-known Impossibility Theorem Arrow proved that no aggregation
procedure can guarantee to satisfy all four conditions. Not
surprisingly, this significant and rather depressing result has attracted
much attention over the years. It suggests that it is impossible to derive
a truly democratic system for resolving differences of opinion. Any
method which is tried will have some shortcoming.
Given that no method can be perfect it is possible to devise an approach
which is reasonably acceptable? Ferrell argues that approval voting is both
simple and robust. In this system individuals vote for all the options
which they consider to be at least just acceptable. The group choice will
then be the option which receives the most votes. Of course, this method
ignores much of the available information about individual preferences.
While you may consider alternatives A and B to be acceptable, you
may have a preference for A. However, by ignoring this information the
method avoids the sort of paradoxical results which we have seen can
occur with other methods.
Aggregating values and utilities
It is important to note that Arrow’s Impossibility Theorem refers only to
situations where individuals have stated the order of their preferences. A
statement giving an individual’s preference order does not tell you about
that person’s intensity of preference for the alternatives. For example,
when considering three possible holiday destinations you may list your
preferences from the best to the worst, as follows:
Rio de Janeiro
San Francisco
Toronto
However, your intensity of preference for Rio de Janeiro may be very
much greater than that for San Francisco, while your preference for
San Francisco may be only slightly greater than that for Toronto. As
we saw in earlier chapters, an individual’s intensity of preference for
an alternative can be measured by determining either the value or, in
the case of uncertainty, the utility of that course of action. The problem
with aggregating the values or utilities of a group of individuals is that
the intensities of preference of the individuals have to be compared. To
illustrate this, let us suppose that a group of two people, A and B, have to
choose between our three holiday destinations. For each person, values
are elicited to measure their relative preference for the destinations.