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On Domains That Admit Well-behaved Strategy-proof Social Choice Functions

  • Shurojit Chatterji

    ()

    (School of Economics, Singapore Management University)

  • Remzi Sanver

    ()

    (Department of Economics, Istanbul Bilgi University)

  • Arunava Sen

    ()

    (Indian Statistical Institute)

In this paper, we investigate domains which admit "well-behaved", strategy-proof social choice functions. We show that if the number of voters is even, then every domain that satisfies a richness condition and admits an anonymous, tops-only, unanimous and strategy-proof social choice function, must be semi-single-peaked. Conversely every semi-single-peaked domain admits an anonymous, tops-only, unanimous and strategy-proof social choice function. Semi-single-peaked domains are generalizations of single-peaked domains on a tree introduced by Demange (1982). We provide sharper versions of the results above when tops-onlyness is replaced by tops-selectivity and the richness condition is weakened.

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Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 07-2010.

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Date of creation: May 2010
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Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:07-2010
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  1. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
  2. Danilov, Vladimir I., 1994. "The structure of non-manipulable social choice rules on a tree," Mathematical Social Sciences, Elsevier, vol. 27(2), pages 123-131, April.
  3. 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.
  4. Berga, Dolors & Serizawa, Shigehiro, 2000. "Maximal Domain for Strategy-Proof Rules with One Public Good," Journal of Economic Theory, Elsevier, vol. 90(1), pages 39-61, January.
  5. Ching, Stephen & Serizawa, Shigehiro, 1998. "A Maximal Domain for the Existence of Strategy-Proof Rules," Journal of Economic Theory, Elsevier, vol. 78(1), pages 157-166, January.
  6. Miguel Ángel Ballester & Guillaume Haeringer, 2006. "A Characterization of Single-Peaked Preferences," Working Papers 273, Barcelona Graduate School of Economics.
  7. Navin Aswal & Shurojit Chatterji & Arunava Sen, 2003. "Dictatorial domains," Economic Theory, Springer, vol. 22(1), pages 45-62, 08.
  8. Shurojit Chatterji & Arunava Sen, 2009. "Tops-Only Domains," Working Papers 06-2009, Singapore Management University, School of Economics.
  9. Alejandro Neme & Jordi MassÔ & Salvador BarberÁ, 1999. "Maximal domains of preferences preserving strategy-proofness for generalized median voter schemes," Social Choice and Welfare, Springer, vol. 16(2), pages 321-336.
  10. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
  11. 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.
  12. Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
  13. Saporiti, Alejandro, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
  14. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
  15. Muller, Eitan, 1982. "Graphs and Anonymous Social Welfare Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 609-22, October.
  16. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  17. Nehring, Klaus & Puppe, Clemens, 2007. "Efficient and strategy-proof voting rules: A characterization," Games and Economic Behavior, Elsevier, vol. 59(1), pages 132-153, April.
  18. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
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