NONDICTATORIALLY INDEPENDENT PAIRS

Suppose that social welfare function f satisfies the Pareto condition and has complete and transitive values. On a domain satisfying the fre e quadruple property, if the outcome set X has m < infinity outcomes, then the set of pairs of distinct alternatives on which f satisfies bo th independence and nondictatorship contains at most the fraction 2/m of all pairs. On a domain satisfying the free six-tuple property, if X is a subset of Euclidean space then the set of pairs on which f satis fies both independence and nondictatorship has Lebesgue measure zero.