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Social choice theory without Pareto: The pivotal voter approach

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  • Miller, Michael K.
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    Abstract

    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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    Bibliographic Info

    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

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    Web page: http://www.elsevier.com/locate/inca/505565

    Related research

    Keywords: Social choice theory Preference aggregation theory Wilson's Theorem Arrow's Theorem Pivotal voters;

    References

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    1. 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.
    2. Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
    3. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    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. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
    6. John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer, vol. 26(1), pages 211-215, 07.
    7. 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.
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    Cited by:
    1. Susumu Cato & Yohei Sekiguchi, 2012. "A generalization of Campbell and Kelly’s trade-off theorem," Social Choice and Welfare, Springer, vol. 38(2), pages 237-246, February.
    2. Jamal Nazrul Islam & Haradhan Kumar Mohajan & Pahlaj Moolio, 2009. "Political Economy and Social Welfare with Voting Procedure," KASBIT Journal of Management & Social Science, Khadim Ali Shah Bukhari Institute of Technology (KASBIT), vol. 2, pages 42-66, December.
    3. Islam, Jamal & Mohajan, Haradhan & Moolio, Pahlaj, 2010. "Methods of voting system and manipulation of voting," MPRA Paper 50854, University Library of Munich, Germany, revised 06 May 2010.
    4. Susumu Cato, 2012. "Social choice without the Pareto principle: a comprehensive analysis," Social Choice and Welfare, Springer, vol. 39(4), pages 869-889, October.
    5. Susumu Cato, 2010. "Brief proofs of Arrovian impossibility theorems," Social Choice and Welfare, Springer, vol. 35(2), pages 267-284, July.
    6. Uuganbaatar Ninjbat, 2012. "Symmetry vs. complexity in proving the Muller-Satterthwaite theorem," Economics Bulletin, AccessEcon, vol. 32(2), pages 1434-1441.
    7. Jamal Nazrul Islam & Haradhan Kumar Mohajan & Pahlaj Moolio, 2009. "Preference of Social Choice in Mathematical Economics," Indus Journal of Management & Social Science (IJMSS), Department of Business Administration, vol. 3(1), pages 18-38, June.
    8. repec:ksb:journl:v:2:y:2009:i:1:p:42-66 is not listed on IDEAS
    9. Mohajan, Haradhan, 2011. "Social welfare and social choice in different individuals’ preferences," MPRA Paper 50851, University Library of Munich, Germany, revised 19 Jun 2011.

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