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Strategy-Proofness and Single-Crossing

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Abstract

This paper analyzes strategy-proof collective choice rules when individuals have single-crossing preferences on a finite and ordered set of social alternatives. It shows that a social choice rule is anonymous, unanimous and strategy-proof on a maximal single-crossing domain if and only if it is an extended median rule with n - 1 fixed ballots located at the end points of the set of alternatives. As a by-product, the paper also proves that strategy-proofness implies the tops-only property. And it offers a strategic foundation for the so called "single-crossing version" of the Median Voter Theorem, by showing that the median ideal point can be implemented in dominant strategies by a direct mechanism in which every individual reveals his true preferences.

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File URL: http://www.wallis.rochester.edu/WallisPapers/wallis_55.pdf
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Bibliographic Info

Paper provided by University of Rochester - Wallis Institute of Political Economy in its series Wallis Working Papers with number WP55.

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Length: 44 pages
Date of creation: Mar 2008
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Handle: RePEc:roc:wallis:wp55

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Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.

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Keywords: Strategy-proofness; single-crossing; median voter; positional dictators;

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References

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  1. Salvador BARBER?Author-Email: salvador.barbera@uab.es & Matthew O. JACKSON, 2003. "Choosing How to Choose: Self-Stable Majority Rules and Constitutions," UFAE and IAE Working Papers 596.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. John A. Weymark, 2004. "Strategy-Proofness and the Tops-Only Property," Vanderbilt University Department of Economics Working Papers 0409, Vanderbilt University Department of Economics, revised Sep 2006.
  3. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
  4. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
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  7. Zhou, Lin, 1991. "Impossibility of Strategy-Proof Mechanisms in Economies with Pure Public Goods," Review of Economic Studies, Wiley Blackwell, vol. 58(1), pages 107-19, January.
  8. Fan-chin Kung, 2004. "An Algorithm for Stable and Equitable Coalition Structures with Public Goods," Game Theory and Information 0409007, EconWPA, revised 05 May 2005.
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  27. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
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Citations

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Cited by:
  1. Alejandro Saporiti & Fernando Tohmé, 2003. "Single-Crossing, Strategic Voting and the Median Choice Rule," CEMA Working Papers: Serie Documentos de Trabajo. 237, Universidad del CEMA.
  2. Franz Dietrich & Christian List, 2007. "Strategy-proof judgment aggregation," LSE Research Online Documents on Economics 5812, London School of Economics and Political Science, LSE Library.
  3. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2009. "Individual versus group strategy-proofness: when do they coincide?," UFAE and IAE Working Papers 761.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. Franz Dietrich & Christian List, 2010. "Majority voting on restricted domains," LSE Research Online Documents on Economics 27902, London School of Economics and Political Science, LSE Library.
  5. Robert Bredereck & Jiehua Chen & Gerhard Woeginger, 2013. "A characterization of the single-crossing domain," Social Choice and Welfare, Springer, vol. 41(4), pages 989-998, October.
  6. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
  7. Javier Perote & Juan Perote-Peña & Marc Vorsatz, 2012. "Strategic behavior in regressions: an experimental," Working Papers 2012-07, FEDEA.
  8. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  9. X. Ruiz del Portal, 2012. "Conditions for incentive compatibility in models with multidimensional allocation functions and one-dimensional types," Review of Economic Design, Springer, vol. 16(4), pages 311-321, December.
  10. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Voting Rules," Working Papers tecipa-493, University of Toronto, Department of Economics.
  11. 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.
  12. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
  13. Goswami, Mridu Prabal & Sen, Arunava & Mitra, Manipushpak, 2014. "Strategy-proofness and Pareto-efficiency in quasi-linear exchange economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
  14. Luis Corchón & José Rueda-Llano, 2008. "Differentiable strategy-proof mechanisms for private and public goods in domains that are not necessarily large or quasi-linear," Review of Economic Design, Springer, vol. 12(4), pages 279-291, December.

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