A majority-rule characterization with multiple extensions

When May's necessary and sufficient conditions for majority rule as a binary voting rule are extended in a natural way to decisions over more than two options, the resulting conditions are consistent with the Borda and Black voting rules, but not with a variety of other voting rules for more than two options. This paper presents an alternative set of necessary and sufficient conditions for binary majority rule, which permits the plurality, Condorcet and (simplified) Dodgson rules, as well as the Borda and Black rules, but not the Copeland or Nanson rules, to be classified as extensions of binary majority rule to decisions over more than two options.I am indebted to Amartya Sen and anonymous referees for helpful suggestions