Opinion Aggregation: Borda and Condorcet Revisited

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 state of opinion. 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 goodness relations of agents in a society, it is not limited to them. In addition to that interpretation, opinions can also be used to represent other forms of comparative assessments emerging from different sources. The main results of the paper provide characterizations of suitably formulated versions of the Borda rule and Condorcet’s majority rule, essential aggregation methods that remain well-defined in our larger context.