An extension and an alternative characterization of May's theorem (Q2241136)

This paper considers the voting scenario in which each voter expresses a level of affinity with a proposal by choosing a value in the set \(\{-j,\dots,-1,0,1,\dots,j\}\), and a decision function derives from these individual votes a collective result, in the same set. Properties of such decision rules are studied. Relations between axioms of neutrality, anonymity, monotonicity, balancedness and of tie-breaking and cancellation properties are discussed. A \(j\)-majority decision function is defined and sets of independent axioms identifying it are presented. The restriction of this characterization for \(j=1\) provides equivalent formulation s of May's theorem.