An extension and an alternative characterization of May’s theorem

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 $${\mathcal {J}}=\{-j,\dots ,-1,0,1,\dots ,j\}$$ J = { - j , ⋯ , - 1 , 0 , 1 , ⋯ , j } , and these individual votes produce a collective result, in the same set $${\mathcal {J}}$$ J , through a decision function. The simple majority, defined for $$j=1$$ 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 $$j=1$$ j = 1 . In this way, this axiomatic characterization meets two goals: it gives a new characterization of the simple majority decision when $$j=1$$ j = 1 and it extends May’s theorem to this broader context.