Social choice theory without Pareto: The pivotal voter approach
This paper extends the pivotal voter approach pioneered by Barberá [Barberá, S., 1980. Pivotal voters: A new proof of Arrow's Theorem. Economics Letters 6, 13-6; Barberá, S., 1983. Strategy-proofness and pivotal voters: A direct proof of the Gibbard-Satterthwaite Theorem. International Economic Review 24, 413-7] to all social welfare functions satisfying independence of irrelevant alternatives. Arrow's Theorem, Wilson's Theorem, and the Muller-Satterthwaite Theorem are all immediate corollaries of the main result. It is further shown that a vanishingly small fraction of pairs of alternatives can be affected in the group preference ordering by multiple individuals, which generalizes each of the above theorems.
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- Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
- Donald Campbell & Jerry Kelly, 2007. "Social welfare functions that satisfy Pareto, anonymity, and neutrality, but not independence of irrelevant alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 69-82, July.
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- Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
- Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
- Barbera, Salvador, 1983. "Strategy-Proofness and Pivotal Voters: A Direct Proof of the Gibbard-Satterthwaite Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(2), pages 413-17, June.
- John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 211-215, 07.
- Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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