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

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

Abstract

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.

Suggested Citation

  • De Donder, Philippe & Le Breton, Michel & Peluso, Eugenio, 2010. "Majority Voting in Multidimensional Policy Spaces: Kramer-Shepsle versus Stackelberg," IDEI Working Papers 593, Institut d'Économie Industrielle (IDEI), Toulouse.
    • Handle: RePEc:ide:wpaper:21845
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    5. Bellani, Luna & Fabella, Vigile Marie & Scervini, Francesco, 2023. "Strategic compromise, policy bundling and interest group power: Theory and evidence on education policy," European Journal of Political Economy, Elsevier, vol. 77(C).
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    8. Dotti, Valerio, 2020. "Income inequality, size of government, and tax progressivity: A positive theory," European Economic Review, Elsevier, vol. 121(C).
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    10. Philippe De Donder & Michel Le Breton & Eugenio Peluso, 2012. "On the (sequential) majority choice of public good size and location," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 457-489, July.
    11. Gregorini, Filippo, 2015. "Political geography and income inequalities," Research in Economics, Elsevier, vol. 69(3), pages 439-452.
    12. Masciandaro, Donato & Passarelli, Francesco, 2013. "Financial systemic risk: Taxation or regulation?," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 587-596.
    13. Bellani, Luna & Fabella, Vigile Marie & Scervini, Francesco, 2020. "Strategic Compromise, Policy Bundling and Interest Group Power," IZA Discussion Papers 13924, Institute of Labor Economics (IZA).
    14. Klaus Schmidt-Hebbel & José Carlos Tello, 2014. "The Political Economy of Growth, Inequality, the Size and Composition of Government Spending," Documentos de Trabajo / Working Papers 2014-380, Departamento de Economía - Pontificia Universidad Católica del Perú.
    15. Sharma, Ajay & Pal, Rupayan, 2019. "Nash equilibrium in tax and public investment competition," International Review of Economics & Finance, Elsevier, vol. 62(C), pages 106-120.
    16. Kirill Borissov & Joseph Hanna & Stéphane Lambrecht, 2019. "Public goods, voting, and growth," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 21(6), pages 1221-1265, December.
    17. Sascha Kurz & Nicola Maaser & Stefan Napel & Matthias Weber, 2014. "Mostly Sunny: A Forecast of Tomorrow's Power Index Research," Tinbergen Institute Discussion Papers 14-058/I, Tinbergen Institute.

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    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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