Self-Selective Social Choice Functions Verify Arrow and Gibbard-Satterthwaite Theorems

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Abstract

This paper introduces a new notion of consistency for social choice functions, called self-selectivity, which requires that a social choice function employed by a society to make a choice from a given alternative set it faces should choose itself from among other rival such functions when it is employed by the society to make this latter choice as well. A unanimous neutral social choice function turns out to be universally self-selective if and only if it is Paretian and satisfies independence of irrelevant alternatives. The neutralunanimous social choice functions whose domains consist of linear order profiles on nonempty sets of any finite cardinality induce a class of social welfare functions that inherit Paretianism and independence of irrelevant alternatives in case the social choice function with which one starts is universally self-selective. Thus, a unanimous and neutral social choice function is universally self-selective if and only if it is dictatorial. Moreover, universal self-selectivity for such functions is equivalent to the conjunction of strategy-proofness and independence of irrelevant alternatives or the conjunction of monotonicity and independence of irrelevant alternatives again.

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