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Abstract

If individuals are never indifferent between distinct alternatives then for any transitive-valued social welfare function satisfying IIA, and any fraction t, either the set of pairs of alternatives that are socially ordered without consulting more than one individual's preferences comprises at least the fraction t of all pairs, or else the fraction of pairs that have their social ordering determined independently of everyone's s preferences exceeds, or is very close to, 1 −t. The Pareto criterion is not imposed. (There is also a version of this result for the domain of preferences that admit indifference.)