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Strategy-Proofness and Single-Crossing

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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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
Handle: RePEc:roc:wallis:wp55
Contact details of provider: Postal:
University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.

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  1. Myerson, Roger B., 2013. "Fundamentals of Social Choice Theory," Quarterly Journal of Political Science, now publishers, vol. 8(3), pages 305-337, 06.
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  8. Le Breton, Michel & Weymark, John A., 1999. "Strategy-proof social choice with continuous separable preferences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 47-85, August.
  9. 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.
  10. Epple, Dennis & Filimon, Radu & Romer, Thomas, 1993. "Existence of voting and housing equilibrium in a system of communities with property taxes," Regional Science and Urban Economics, Elsevier, vol. 23(5), pages 585-610, November.
  11. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  12. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
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  14. Westhoff, Frank, 1977. "Existence of equilibria in economies with a local public good," Journal of Economic Theory, Elsevier, vol. 14(1), pages 84-112, February.
  15. 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.
  16. List, Christian, 2003. "A possibility theorem on aggregation over multiple interconnected propositions," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 1-13, February.
  17. 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.
  18. John A. Weymark, 2008. "Strategy-Proofness and the Tops-Only Property," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(1), pages 7-26, 02.
  19. Demange, G., 1991. "Intermediate Preferences and Stable Coalition Structures," DELTA Working Papers 91-16, DELTA (Ecole normale supérieure).
  20. Jon Eguia, 2007. "Citizen candidates under uncertainty," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(2), pages 317-331, September.
  21. Dennis Epple & Richard Romano & Holger Sieg, 2006. "Admission, Tuition, and Financial Aid Policies in the Market for Higher Education," Econometrica, Econometric Society, vol. 74(4), pages 885-928, 07.
  22. Lin Zhou, 1991. "Impossibility of Strategy-Proof Mechanisms in Economies with Pure Public Goods," Review of Economic Studies, Oxford University Press, vol. 58(1), pages 107-119.
  23. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
  24. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
  25. Donald E. Campbell & Jerry S. Kelly, 2003. "A strategy-proofness characterization of majority rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 557-568, October.
  26. Rothstein, Paul, 1991. "Representative Voter Theorems," Public Choice, Springer, vol. 72(2-3), pages 193-212, December.
  27. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
  28. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  29. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
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