On the indicator function of the plurality function

Abstract If each of a group of ‘experts’ or ‘voters’, human or artificial, gives his or her first choice from among a set of alternatives A , a consensus function assigns to each such set of choices a subset of A called the group's consensus. The plurality function chooses for the consensus all alternatives that receive the largest number of first choices. We state a characterization of the plurality function interpreted as giving a vector of 0's and 1's, with the 1 representing membership in the consensus subset. The problem of generalizing this result in various ways gives new insight into the plurality function and leads to the problem of solving an interesting new functional equation.