Fuzzy Sets and Social Choice

Abstract

Choosing between alternative courses of action presupposes preference. Individual preference appears as a primitive notion with little need for elaboration. Mathematically, it is simply expressed by a complete (or, sometimes, only partial) reflexive antisymmetric and transitive ordering over a set (A) of ‘objects’ which are available for choice. If we wish, we can even consider the derived linear ordering over the quotient set formed by partitioning (A) into a set of ‘indifference classes.’ Even though individuals do seem to contradict some of their own previous choices at times, we do not wish to examine such refinements here. In a static context, it is not an oversimplification to say that individual choices are of the {Yes.No} (0,1) type. Can we, safely, assume that group choices are also that clear-cut? Clearly not. A cursory examination of the history of collective decisions should suffice to convince us of the fuzziness of group preferences.

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