An extension and an alternative characterization of May’s theorem

Abstract

The context of this work is a voting scenario in which each voter expresses his/her level of affinity about a proposal, by choosing a value in the set J={-j,…,-1,0,1,…,j}, and these individual votes produce a collective result, in the same set J, through a decision function. The simple majority, defined for j=1, is a widely used example of such a decision function. In this paper, a set of independent axioms is proved to uniquely characterize the j-majority decision function. The j-majority decision is defined for any positive integer j, and it coincides with the simple majority decision when j=1. In this way, this axiomatic characterization meets two goals: it gives a new characterization of the simple majority decision when j=1 and it extends May’s theorem to this broader context.