Social Indeterminacy

Gil Kalai ()

Discussion Paper Series from The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem

Abstract: An extension of Condorcet's paradox by McGarvey (1953) asserts that for every asymmetric relation R on a finite set of candidates there is a strict-preferences voter profile that has the relation R as its strict simple majority relation. We prove that McGarvey's theorem can be extended to arbitrary neutral monotone social welfare functions which can be described by a strong simple game G if the voting power of each individual, measured by the it Shapley-Shubik power index, is sufficiently small. Our proof is based on an extension to another classic result concerning the majority rule. Condorcet studied an election between two candidates in which the voters' choices are random and independent and the probability of a voter choosing the first candidate is p > 1/2. Condorcet's Jury Theorem asserts that if the number of voters tends to infinity then the probability that the first candidate will be elected tends to one. We prove that this assertion extends to a sequence of arbitrary monotone strong simple games if and only if the maximum voting power for all individuals tends to zero.

Keywords: social choice; information aggregation; Arrow's theorem; simple games; the Shapley-Shubik power index; threshold phenomena (search for similar items in EconPapers)
JEL-codes: C71 D71 D72 D80 (search for similar items in EconPapers)
Pages: 38 pages
Date: 2004-06
New Economics Papers: this item is included in nep-cdm and nep-dcm
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Citations: View citations in EconPapers (5)

Published in Econometrica, 2004, vol. 72, pp. 1565-1581.
Published in The Economic Quarterly, 2003, vol. 4, pp. 771-780.

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