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Strategy-Proofness and Single-Crossing

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Abstract

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.

Suggested Citation

  • Alejandro Saporiti, 2007. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP48, University of Rochester - Wallis Institute of Political Economy.
  • Handle: RePEc:roc:wallis:wp48
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    1. 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.
    2. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
    3. Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 363-383, April.
    4. 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, February.
    5. 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, August.
    6. 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.
    7. Salvador Barbera & Matthew O. Jackson, 2004. "Choosing How to Choose: Self-Stable Majority Rules and Constitutions," The Quarterly Journal of Economics, Oxford University Press, vol. 119(3), pages 1011-1048.
    8. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
    9. Rothstein, Paul, 1991. "Representative Voter Theorems," Public Choice, Springer, vol. 72(2-3), pages 193-212, December.
    10. Myerson, Roger B., 2013. "Fundamentals of Social Choice Theory," Quarterly Journal of Political Science, now publishers, vol. 8(3), pages 305-337, June.
    11. 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.
    12. List, Christian, 2003. "A possibility theorem on aggregation over multiple interconnected propositions," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 1-13, February.
    13. 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.
    14. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    15. 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, July.
    16. 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.
    17. 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.
    18. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    19. 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.
    20. 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.
    21. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    22. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
    23. 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.
    24. 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 914-927, October.
    25. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
    26. 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.
    27. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
    28. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    29. 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.
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    More about this item

    Keywords

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

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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