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Social choice theory without Pareto: The pivotal voter approach

  • Miller, Michael K.
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    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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    File URL: http://www.sciencedirect.com/science/article/B6V88-4VRX63C-1/2/1bb6a38074ce45e57d03452dc836d184
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    Article provided by Elsevier in its journal Mathematical Social Sciences.

    Volume (Year): 58 (2009)
    Issue (Month): 2 (September)
    Pages: 251-255

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    Handle: RePEc:eee:matsoc:v:58:y:2009:i:2:p:251-255
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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    1. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
    2. Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
    3. 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.
    4. 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.
    5. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    6. 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, vol. 29(1), pages 69-82, July.
    7. John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer, vol. 26(1), pages 211-215, 07.
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