Aggregating Opinions

Abstract

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 an aggregate relation on the set of alternatives to every possible multiset of opinions. Our primary motivation is to extend the standard model of social choice theory to a more general one in which no specific reference to agents generating or holding opinions is needed. 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 emerging from different sources. The main result of the paper provides a characterization of a suitably formulated version of the Borda rule, an essential aggregation method that remains well-defined in our larger context.