A Unifying Impossibility Theorem
AbstractThis paper considers social choice correspondences assigning a choice set to each non-empty subset of social alternatives. We impose three requirements on these correspondences: unanimity, independence of preferences over infeasible alternatives and choice consistency with respect to choices out of all possible alternatives. With more than three social alternatives and the universal preference domain, any social choice correspondence that satisfies our requirements is serially dictatorial. A number of known impossibility theorems â€” including Arrowâ€™s Impossibility Theorem, the Muller-Satterthwaite Theorem and the impossibility theorem under strategic candidacy â€” follow as corollaries. Our new proof highlights the common logical underpinnings behind these theorems.
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Bibliographic InfoPaper provided by School of Economics, University of Queensland, Australia in its series Discussion Papers Series with number 448.
Date of creation: 04 Jan 2012
Date of revision:
Other versions of this item:
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-01-10 (All new papers)
- NEP-CDM-2012-01-10 (Collective Decision-Making)
- NEP-MIC-2012-01-10 (Microeconomics)
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- Ning Yu, 2012. "A one-shot proof of Arrow’s impossibility theorem," Economic Theory, Springer, vol. 50(2), pages 523-525, June.
- Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001.
"Strategic Candidacy and Voting Procedures,"
Econometric Society, vol. 69(4), pages 1013-37, July.
- Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer, vol. 19(3), pages 569-580.
- Eraslan, H.Hulya & McLennan, Andrew, 2004. "Strategic candidacy for multivalued voting procedures," Journal of Economic Theory, Elsevier, vol. 117(1), pages 29-54, July.
- Gevers, Louis, 1979. "On Interpersonal Comparability and Social Welfare Orderings," Econometrica, Econometric Society, vol. 47(1), pages 75-89, January.
- 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.
- Karni, Edi & Schmeidler, David, 1976. "Independence of nonfeasible alternatives, and independence of nonoptimal alternatives," Journal of Economic Theory, Elsevier, vol. 12(3), pages 488-493, June.
- Barbera, S. & Peleg, B., 1988. "Strategy-Proof Voting Schemes With Continuous Preferences," UFAE and IAE Working Papers 91.88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2001. "Strategy-proof Social Choice Correspondences," Journal of Economic Theory, Elsevier, vol. 101(2), pages 374-394, December.
- Lars Ehlers & John A. Weymark, 2003.
"Candidate stability and nonbinary social choice,"
Springer, vol. 22(2), pages 233-243, 09.
- EHLERS, Lars & WEYMARK, John A., 2001. "Candidate Stability and Nonbinary Social Choice," Cahiers de recherche 2001-30, Universite de Montreal, Departement de sciences economiques.
- John A. Weymark, 2000. "Candidate Stability and Nonbinary Social Choice," Vanderbilt University Department of Economics Working Papers 0029, Vanderbilt University Department of Economics, revised Feb 2001.
- Lars Ehlers & John A. Weymark, 2001. "Candidate Stability and Nonbinary Social Choice," Vanderbilt University Department of Economics Working Papers 0113, Vanderbilt University Department of Economics.
- Kirman, Alan P. & Sondermann, Dieter, 1972.
"Arrow's theorem, many agents, and invisible dictators,"
Journal of Economic Theory,
Elsevier, vol. 5(2), pages 267-277, October.
- KIRMAN, Alan P. & SONDERMANN, Dieter, . "Arrow's theorem, many agents, and indivisible dictators," CORE Discussion Papers RP -118, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer, vol. 26(1), pages 211-215, 07.
- 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.
- Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
- Shino Takayama & Akira Yokotani, 2014. "Serial Dictatorship with Infinitely Many Agents," Discussion Papers Series 503, School of Economics, University of Queensland, Australia.
- Priscilla Man & Shino Takayama, 2013. "A Unifying Impossibility Theorem for Compact Metricsocial Alternatives Space," Discussion Papers Series 477, School of Economics, University of Queensland, Australia.
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