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Strategy-Proofness and the Tops-Only Property

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  • John A. Weymark

    ()
    (Department of Economics, Vanderbilt University)

Abstract

A social choice function satisfies the tops-only property if the chosen alternative only depends on each person's report of his most-preferred alternatives on the range of this function. On many domains, strategy-proofness implies the tops-only property, provided that the range of the social choice function satisfies some regularity condition. The existing proofs of this result are model specific. In this article, a general proof strategy is proposed for showing that a strategy-proof social choice function satisfies the tops-only property when everyone has the same set of admissible preferences.

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File URL: http://www.accessecon.com/pubs/VUECON/vu04-w09R.pdf
File Function: Revision, 2006
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Bibliographic Info

Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0409.

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Date of creation: Apr 2004
Date of revision: Sep 2006
Handle: RePEc:van:wpaper:0409

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Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

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Keywords: Social choice; strategy-proofness; option sets; tops-only property;

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  1. 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.
  2. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  3. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  4. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-81, April.
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  6. Shigehiro Serizawa, 1999. "Strategy-Proof and Symmetric Social Choice Functions for Public Good Economies," Econometrica, Econometric Society, vol. 67(1), pages 121-146, January.
  7. Ehlers, Lars & Peters, Hans & Storcken, Ton, 2002. "Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 105(2), pages 408-434, August.
  8. Barbera, S. & Masso, J. & Neme, A., 1992. "Voting Under Constraints," UFAE and IAE Working Papers 200.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  9. 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).
  10. 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.
  11. Barbera, S. & Sonnenschein, H., 1988. "Voting By Quota And Committee," UFAE and IAE Working Papers 95-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  12. Salvador Barberà, 2001. "An introduction to strategy-proof social choice functions," Social Choice and Welfare, Springer, vol. 18(4), pages 619-653.
  13. Salvador Barbera & Matthew Jackson, 1991. "A Characterization of Strategy-Proof Social Choice Functions for Economies with Pure Public Goods," Discussion Papers 964, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  15. Satterthwaite, Mark A & Sonnenschein, Hugo, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Wiley Blackwell, vol. 48(4), pages 587-97, October.
  16. Dutta, Bhaskar & Peters, Hans & Sen, Arunava, 2002. "Strategy-Proof Probabilistic Mechanisms in Economies with Pure Public Goods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 392-416, October.
  17. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December.
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  19. Le Breton, M. & Sen, A., 1995. "Strategyproofness and decomposability : Weak Orderings," G.R.E.Q.A.M. 95a38, Universite Aix-Marseille III.
  20. Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990. "Voting by Committees," Cowles Foundation Discussion Papers 941, Cowles Foundation for Research in Economics, Yale University.
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Citations

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Cited by:
  1. Debasis Mishra & Anup Pramanik & Souvik Roy, 2013. "Implementation in multidimensional domains with ordinal restrictions," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 13-07, Indian Statistical Institute, New Delhi, India.
  2. Shurojit Chatterji & Arunava Sen, 2011. "Tops-only domains," Economic Theory, Springer, vol. 46(2), pages 255-282, February.
  3. M. Sanver, 2009. "Strategy-proofness of the plurality rule over restricted domains," Economic Theory, Springer, vol. 39(3), pages 461-471, June.
  4. Alejandro Saporiti, 2008. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP55, University of Rochester - Wallis Institute of Political Economy.
  5. Toyotaka Sakai & Takuma Wakayama, 2012. "Strategy-proofness, tops-only, and the uniform rule," Theory and Decision, Springer, vol. 72(3), pages 287-301, March.
  6. Walter Bossert & John A. Weymark, 2006. "Social Choice: Recent Developments," Vanderbilt University Department of Economics Working Papers 0603, Vanderbilt University Department of Economics.
  7. Donald Campbell & Jerry Kelly, 2013. "Relaxing IIA and the effect on individual power," Review of Economic Design, Springer, vol. 17(3), pages 165-181, September.
  8. Debasis Mishra & Souvik Roy, 2011. "Strategy-proof partitioning," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 11-06, Indian Statistical Institute, New Delhi, India.
  9. John Weymark, 2011. "A unified approach to strategy-proofness for single-peaked preferences," SERIEs, Spanish Economic Association, vol. 2(4), pages 529-550, December.

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