A Note on Impossibility Theorems and Seniority Rules

The purpose of a social choice rule is to resolve conflicts among the preferences of a group of individuals. We should therefore require a social choice rules not to remain indecisive between alternatives for which individuals have conflicting preferences. Suppose we also adopt the requirements of a universal domain, strict Pareto optimality and independence of irrelevant alternatives. We then obtain the existence of a dictatorship (for binary choices) already under the weak consistency assumption that the group's choice function must always generate a preference relation that is acyclical over triples of alternatives. By contrast to other theorems, this results holds without any restrictions on the size of the group and without the axiom of positive responsiveness. Under the same consistency condition, we furthermore obtain an axiomatic characterization of seniority rules, also known as lexical dictatorships.