Aggregating Opinions

Abstract

In a world admitting a fixed finite set of alternatives, an opinion is an ordered pair of alternatives. Such a pair expresses the idea that one alternative is superior to another in some sense, and an opinion aggregator assigns a social relation on the set of alternatives to every possible multiset of opinions. Our primary motivation is to extend some basic results of social choice theory to a more general model in which no specific reference to agents generating or holding opinions is needed. It turns out that, although our analysis has some bearing on those cases where opinions reflect the preferences of agents in a society, it is not limited to them. In addition to the preference interpretation, opinions can also be used to represent other forms of comparative assessments. The main results of the paper provide characterizations of suitably defined versions of the Borda rule and the majority rule.