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Majority Voting in Multidimensional Policy Spaces: Kramer-Shepsle versus Stackelberg

  • De Donder, Philippe
  • Le Breton, Michel
  • Peluso, Eugenio

We study majority voting over a bidimensional policy space when the voters' type space is either uni- or bidimensional. We show that a Condorcet winner fails to generically exist even with a unidimensional type space. We then study two voting procedures widely used in the literature. The Stackelberg (ST) procedure assumes that votes are taken one dimension at a time according to an exogenously specified sequence. The Kramer-Shepsle (KS) procedure also assumes that votes are taken separately on each dimension, but not in a sequential way. A vector of policies is a Kramer-Shepsle equilibrium if each component coincides with the majority choice on this dimension given the other components of the vector. We study the existence and uniqueness of the ST and KS equilibria, and we compare them, looking e.g. at the impact of the ordering of votes for ST and identifying circumstances under which ST and KS equilibria coincide. In the process, we state explicitly the assumptions on the utility function that are needed for these equilibria to be well behaved. We especially stress the importance of single crossing conditions, and we identify two variants of these assumptions: a marginal version that is imposed on all policy dimensions separately, and a joint version whose definition involves both policy dimensions.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 7646.

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Date of creation: Jan 2010
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Handle: RePEc:cpr:ceprdp:7646
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  1. John Duggan, . "Non-Cooperative Games Among Groups," Wallis Working Papers WP21, University of Rochester - Wallis Institute of Political Economy.
  2. Filippo Gregorini, 2009. "Political Geography and Income Inequalities," Working Papers 152, University of Milano-Bicocca, Department of Economics, revised Feb 2009.
  3. Helmuth Cremer & Philippe De Donder & Firouz Gahvari, 2004. "Taxes, Budgetary Rule and Majority Voting," Public Choice, Springer, vol. 119(3_4), pages 335-358, 06.
  4. Filippo Gregorini, 2007. "Political Geography and Income Inequalities," DISCE - Quaderni dell'Istituto di Teoria Economica e Metodi Quantitativi itemq0746, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).
  5. Philippe De Donder & Jean Hindriks, 1998. "The political economy of targeting," Public Choice, Springer, vol. 95(1), pages 177-200, April.
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  8. Banks, Jeffrey & Duggan, John & Le Breton, Michel, 2003. "Social Choice and Electoral Competition in the General Spatial Model," IDEI Working Papers 188, Institut d'Économie Industrielle (IDEI), Toulouse.
  9. Baqir, Reza & Easterly, William & Alesina, Alberto, 1999. "Public Goods and Ethnic Divisions," Scholarly Articles 4551797, Harvard University Department of Economics.
  10. Thomas J. Nechyba, 1996. "Local Property and State Income Taxes: The Role of Interjurisdictional Competition and Collusion," NBER Working Papers 5419, National Bureau of Economic Research, Inc.
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  12. Diba, Behzad & Feldman, Allan M., 1984. "Utility functions for public outputs and majority voting," Journal of Public Economics, Elsevier, vol. 25(1-2), pages 235-243, November.
  13. Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, vol. 40(1), pages 147-57, January.
  14. repec:hrv:faseco:4553034 is not listed on IDEAS
  15. Perroni, Carlo & Scharf, Kimberly A, 2001. "Tiebout with Politics: Capital Tax Competition and Constitutional Choices," Review of Economic Studies, Wiley Blackwell, vol. 68(1), pages 133-54, January.
  16. Federico Etro, 2006. "Political geography," Public Choice, Springer, vol. 127(3), pages 321-343, June.
  17. Sadanand, Asha B & Williamson, John M, 1991. "Equilibrium in a Stock Market Economy with Shareholder Voting," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(1), pages 1-35, February.
  18. 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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