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.