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Strategy-Proofness and Single-Crossing

This paper analyzes collective choices in a society with strategic voters and single-crossing preferences. It shows that, in addition to single-peakedness, single-crossingness is another meaningful domain which guarantees the existence of non-manipulable social choice functions. A social choice function is shown to be anonymous, unanimous and strategy-proof on single-crossing domains if and only if it is an extended median rule with n-1 parameters distributed on the end points of the feasible set of alternatives. Such rules are known as positional dictators, and they include the median choice rule as a particular case. As a by-product, the paper also provides an 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 through a simple mechanism in which each agent honestly reveals his preferences.

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File URL: http://www.wallis.rochester.edu/WallisPapers/wallis_48.pdf
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Paper provided by University of Rochester - Wallis Institute of Political Economy in its series Wallis Working Papers with number WP48.

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Length: 23 pages
Date of creation: Oct 2007
Date of revision:
Handle: RePEc:roc:wallis:wp48
Contact details of provider: Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.

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  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. 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.
  3. Dennis Epple & Richard Romano & Holger Sieg, . "Admission, Tuition, and Financial Aid Policies in the Market for Higher Education," GSIA Working Papers 2003-04, Carnegie Mellon University, Tepper School of Business.
  4. Roger B. Myerson, 1996. "Fundamentals of Social Choice Theory," Discussion Papers 1162, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Salvador Barbera & Matthew O. Jackson, 2004. "Choosing How to Choose: Self-Stable Majority Rules and Constitutions," The Quarterly Journal of Economics, MIT Press, vol. 119(3), pages 1011-1048, August.
  6. Dennis Epple & Thomas Romer & Holger Sieg, 2001. "Interjurisdictional Sorting and Majority Rule: An Empirical Analysis," Econometrica, Econometric Society, vol. 69(6), pages 1437-1465, November.
  7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  8. Meltzer, Allan H & Richard, Scott F, 1981. "A Rational Theory of the Size of Government," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 914-27, October.
  9. Fan-Chin Kung, 2006. "An Algorithm for Stable and Equitable Coalition Structures with Public Goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(3), pages 345-355, 08.
  10. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  11. 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.
  12. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  13. List, Christian, 2003. "A possibility theorem on aggregation over multiple interconnected propositions," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 1-13, February.
  14. Rothstein, Paul, 1991. " Representative Voter Theorems," Public Choice, Springer, vol. 72(2-3), pages 193-212, December.
  15. Barbera, S. & Gul, F. & Stacchetti, E., 1992. "Generalized Median Voter Schemes and Committees," UFAE and IAE Working Papers 184.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  16. 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.
  17. 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.
  18. 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.
  19. Calabrese, Stephen & Epple, Dennis & Romer, Thomas & Sieg, Holger, 2006. "Local public good provision: Voting, peer effects, and mobility," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 959-981, August.
  20. Jon Eguia, 2007. "Citizen candidates under uncertainty," Social Choice and Welfare, Springer, vol. 29(2), pages 317-331, September.
  21. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
  22. Donald E. Campbell & Jerry S. Kelly, 2003. "A strategy-proofness characterization of majority rule," Economic Theory, Springer, vol. 22(3), pages 557-568, October.
  23. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  24. 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.
  25. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
  26. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
  27. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
  28. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
  29. 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.
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