A short step between democracy and dictatorship

Abstract

When preferences are defined over two alternatives and societies are variable, the group formed by the relative majority rule, the unanimity rule, the dictatorial rules, and the strongly dictatorial rules is characterized in terms of five axioms: unanimity, reducibility, substitutability, exchangeability, and parity. This result is used to provide characterizations of each of these rules by postulating separating axioms, that is, an axiom and its negation. Such axioms identify traits specifically differentiating a type of rule from the other types. For instance, majority differs from strong dictatorship in the existence of a society for which collective indifference should be a less likely outcome than the strict preference of one alternative over the other. As a second example, the difference between majority and strong dictatorship can be traced back to the requirement that the likelihood of collective indifference diminishes with the size of society.