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Social choice theory without Pareto: The pivotal voter approach

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  • Miller, Michael K.

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.

Suggested Citation

  • Miller, Michael K., 2009. "Social choice theory without Pareto: The pivotal voter approach," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 251-255, September.
    • Handle: RePEc:eee:matsoc:v:58:y:2009:i:2:p:251-255
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    References listed on IDEAS

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    1. 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 413-417, June.
    2. 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.
    3. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
    4. 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.
    5. 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.
    6. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    7. Salvador Barberà, 2001. "An introduction to strategy-proof social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 619-653.
    8. 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, July.
    9. Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
    10. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Cited by:

    1. Wesley H. Holliday & Mikayla Kelley, 2020. "A note on Murakami’s theorems and incomplete social choice without the Pareto principle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(2), pages 243-253, August.
    2. Susumu Cato & Yohei Sekiguchi, 2012. "A generalization of Campbell and Kelly’s trade-off theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 237-246, February.
    3. 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.
    4. Susumu Cato, 2010. "Brief proofs of Arrovian impossibility theorems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 267-284, July.
    5. Susumu Cato, 2012. "Social choice without the Pareto principle: a comprehensive analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 869-889, October.
    6. 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.
    7. Mohajan, Haradhan, 2011. "Social welfare and social choice in different individuals’ preferences," MPRA Paper 50851, University Library of Munich, Germany, revised 19 Jun 2011.
    8. Jamal Nazrul Islam & Haradhan Kumar Mohajan & Pahlaj Moolio, 2009. "Political Economy and Social Welfare with Voting Procedure," KASBIT Business Journals (KBJ), Khadim Ali Shah Bukhari Institute of Technology (KASBIT), vol. 2, pages 42-66, December.
    9. Susumu Cato, 2016. "Weak independence and the Pareto principle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 295-314, August.
    10. Uuganbaatar Ninjbat, 2012. "Symmetry vs. complexity in proving the Muller-Satterthwaite theorem," Economics Bulletin, AccessEcon, vol. 32(2), pages 1434-1441.
    11. repec:ksb:journl:v:2:y:2009:i:1:p:42-66 is not listed on IDEAS

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