Lebesgue Measure and Social Choice Trade-offs

Donald E Campbell and Jerry S Kelly

Economic Theory, 1995, vol. 5, issue 3, 445-59

Abstract: An Arrovian social choice rule is a social welfare function satisfying independence of irrelevant alternatives and transitivity of social preference. Assume a measurable outcome space X with its (Lebesgue) measure normalized to unity. For any Arrovian rule and any fraction t, either some individual dictates over a subset of X of measure t or more, or at least a fraction 1 - t of the pairs of distinct alternatives have their social ordering fixed independently of individual preferences. Also, for any positive integer "Beta" (less than the total number of individuals), there is some subset H of society consisting of all but "Beta" persons such that the fraction of outcome pairs (x,y) that are social ranked without consulting the preferences of anyone in H, whenever no individual is indifferent between x and y, is at least 1 - 1/4("Beta").

Date: 1995
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