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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.

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File URL: http://www.wallis.rochester.edu/WallisPapers/wallis_48.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 WP48.

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Length: 23 pages
Date of creation: Oct 2007
Date of revision:
Handle: RePEc:roc:wallis:wp48

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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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  4. 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.
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  22. Eguia, Jon X., 2005. "Citizen candidates under uncertainty," Working Papers 1233, California Institute of Technology, Division of the Humanities and Social Sciences.
  23. Christian List, 2002. "A Possibility Theorem on Aggregation Over Multiple Interconnected Propositions," Economics Series Working Papers 123, University of Oxford, Department of Economics.
  24. 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.
  25. 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.
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  27. 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.
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Citations

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Cited by:
  1. 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.
  2. 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).
  3. 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.
  4. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
  5. 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.
  6. Christian List & Ben Polak, 2010. "Introduction to Judgment Aggregation," Levine's Working Paper Archive 661465000000000006, David K. Levine.
  7. 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.
  8. 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.
  9. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Voting Rules," Working Papers tecipa-493, University of Toronto, Department of Economics.
  10. 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.
  11. Salvador Barberà, 2010. "Strategy-proof social choice," Working Papers 420, Barcelona Graduate School of Economics.
  12. Javier Perote & Juan Perote-Peña & Marc Vorsatz, 2012. "Strategic behavior in regressions: an experimental," Working Papers 2012-07, FEDEA.
  13. 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.
  14. 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.

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