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Tops-Only Domains

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  • Shurojit Chatterji

    ()
    (School of Economics, Singapore Management University)

  • Arunava Sen

    ()
    (Indian Statistical Institute)

Abstract

In this paper we consider the standard voting model with a finite set of alternatives A and n voters and address the following question: what are the characteristics of domains D that induce the property that every strategy-proof social choice function f : Dn ! A satisfying unanimity, has the tops-only property? We first impose a minimal richness condition which ensures that for every alternative a, there exists an admissible ordering where a is maximal. We identify conditions on D that are sufficient for strategy-proofness and unanimity to imply tops onlyness in the general case of n voters and in the special case, n = 2. We provide an algorithm for constructing tops-only domains from connected graphs with elements of A as nodes. We provide several applications of our results. Finally, we relax the minimal richness assumption and partially extend our results.

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Bibliographic Info

Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 06-2009.

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Length: 32 pages
Date of creation: Feb 2009
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:06-2009

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References

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  1. Salvador BARBER? & Jordi MassóAuthor-Email: jordi.masso@uab.es & Alejandro NEME, 2001. "Voting by Committees under Constraints," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 501.01, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 1997. "Voting under Constraints," Journal of Economic Theory, Elsevier, vol. 76(2), pages 298-321, October.
  3. Barbera, S. & Gul, F. & Stacchetti, E., 1992. "Generalized Median Voter Schemes and Committees," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 184.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
  5. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2001. "Strategy-proof Social Choice Correspondences," Journal of Economic Theory, Elsevier, vol. 101(2), pages 374-394, December.
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  11. ASWAL, Navin & CHATTERJI, Shurojit & SEN, Arunava, 1999. "Dictatorial domains," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1999040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer, Springer, vol. 19(3), pages 569-580.
  13. Benoit, Jean-Pierre, 2002. "Strategic Manipulation in Voting Games When Lotteries and Ties Are Permitted," Journal of Economic Theory, Elsevier, vol. 102(2), pages 421-436, February.
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  16. John Duggan & Thomas Schwartz, 2000. "Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized," Social Choice and Welfare, Springer, Springer, vol. 17(1), pages 85-93.
  17. Özyurt, Selçuk & Sanver, M. Remzi, 2009. "A general impossibility result on strategy-proof social choice hyperfunctions," Games and Economic Behavior, Elsevier, vol. 66(2), pages 880-892, July.
  18. Klaus, Bettina & Peters, Hans & Storcken, Ton, 1997. "Strategy-proof division of a private good when preferences are single-dipped," Economics Letters, Elsevier, vol. 55(3), pages 339-346, September.
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Citations

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Cited by:
  1. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2011. "Two Necessary Conditions for Strategy-Proofness: on What Domains are they also Sufficient?," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 892.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Matías Núñez, 2014. "The strategic sincerity of Approval voting," Economic Theory, Springer, Springer, vol. 56(1), pages 157-189, May.
  3. Shurojit Chatterji & Arunava Sen & Huaxia Zeng, 2012. "Random Dictatorship Domains," Working Papers, Singapore Management University, School of Economics 27-2012, Singapore Management University, School of Economics.
  4. Chatterji, Shurojit & Sanver, Remzi & Sen, Arunava, 2013. "On domains that admit well-behaved strategy-proof social choice functions," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1050-1073.
  5. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Mechanism Design without Money," Working Papers tecipa-481, University of Toronto, Department of Economics.
  6. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2013. "Egalitarian Equivalence And Strategyproofness In The Queueing Problem," Discussion Papers in Economics 13/16, Department of Economics, University of Leicester.
  7. Sato, Shin, 2013. "A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one," Journal of Economic Theory, Elsevier, vol. 148(1), pages 259-278.
  8. Debasis Mishra & Souvik Roy, 2011. "Strategy-proof partitioning," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers, Indian Statistical Institute, New Delhi, India 11-06, Indian Statistical Institute, New Delhi, India.
  9. Shin Sato, 2010. "Circular domains," Review of Economic Design, Springer, Springer, vol. 14(3), pages 331-342, September.

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