Econometrica: Sep 2004, Volume 72, Issue 5

Social Indeterminacy
p. 1565-1581

Gil Kalai

An extension of Condorcet's paradox by McGarvey (1953) asserts that for every asymmetric relation on a finite set of candidates there is a strict‐preferences voter profile that has the relation as its strict simple majority relation. We prove that McGarvey's theorem can be extended to arbitrary neutral monotone social welfare functions that can be described by a strong simple game if the voting power of each individual, measured by the , is sufficiently small.

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