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A Unifying Impossibility Theorem

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This 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 — including Arrow’s Impossibility Theorem, the Muller-Satterthwaite Theorem and the impossibility theorem under strategic candidacy — follow as corollaries. Our new proof highlights the common logical underpinnings behind these theorems.

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Paper provided by School of Economics, University of Queensland, Australia in its series Discussion Papers Series with number 448.

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Date of creation: 04 Jan 2012
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Handle: RePEc:qld:uq2004:448

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  1. John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer, vol. 26(1), pages 211-215, 07.
  2. Lars Ehlers & John A. Weymark, 2003. "Candidate stability and nonbinary social choice," Economic Theory, Springer, vol. 22(2), pages 233-243, 09.
  3. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2001. "Strategy-proof Social Choice Correspondences," Journal of Economic Theory, Elsevier, vol. 101(2), pages 374-394, December.
  4. Gevers, Louis, 1979. "On Interpersonal Comparability and Social Welfare Orderings," Econometrica, Econometric Society, vol. 47(1), pages 75-89, January.
  5. 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.
  6. Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer, vol. 19(3), pages 569-580.
  7. 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.
  8. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  9. Priscilla Man & Shino Takayama, 2012. "A Unifying Impossibility Theorem," Discussion Papers Series 448, School of Economics, University of Queensland, Australia.
  10. Ning Yu, 2012. "A one-shot proof of Arrow’s impossibility theorem," Economic Theory, Springer, vol. 50(2), pages 523-525, June.
  11. 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.
  12. 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).
  13. 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).
  14. Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001. "Strategic Candidacy and Voting Procedures," Econometrica, Econometric Society, vol. 69(4), pages 1013-37, July.
  15. 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.
  16. Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
  17. Eraslan, H.Hulya & McLennan, Andrew, 2004. "Strategic candidacy for multivalued voting procedures," Journal of Economic Theory, Elsevier, vol. 117(1), pages 29-54, July.
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Cited by:
  1. Shino Takayama & Akira Yokotani, 2014. "Serial Dictatorship with Infinitely Many Agents," Discussion Papers Series 503, School of Economics, University of Queensland, Australia.
  2. Matías Núñez, 2014. "The strategic sincerity of Approval voting," Economic Theory, Springer, vol. 56(1), pages 157-189, May.
  3. Priscilla Man & Shino Takayama, 2012. "A Unifying Impossibility Theorem," Discussion Papers Series 448, School of Economics, University of Queensland, Australia.
  4. 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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