Suppose a social welfare function f has complete and transitive values and the set X of outcomes has size m3. If the domain D of f has the free quadruple property then the fraction of pairs on which f satisfies nondictatorship, independence, and Pareto is less than or equal to $\left...

We introduce the notion of a quota pair system and show that any social choice procedure, where there are exactly two alternatives and a fixed number of voters, satisfies anonymity and monotonicity if and only if it is uniquely determined by a quota pair system.

In the case of two alternatives, elementary counting techniques are used to determine the number of aggregation rules that satisfy anonymity and neutrality.

The notion of a decisive family of voters has played an important role in the analysis of various consensus functions defined on preference profiles. This role remains when the domain shifts to profiles of hierarchical classifications. The main result of this paper is a characterization of...