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

Author

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  • PHILIPPE DE DONDER
  • MICHEL LE BRETON
  • EUGENIO PELUSO

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.
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Suggested Citation

  • Philippe De Donder & Michel Le Breton & Eugenio Peluso, 2012. "Majority Voting in Multidimensional Policy Spaces: Kramer–Shepsle versus Stackelberg," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 14(6), pages 879-909, December.
    • Handle: RePEc:bla:jpbect:v:14:y:2012:i:6:p:879-909
    DOI: jpet.12001
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    Cited by:

    1. Gregorini, Filippo, 2015. "Political geography and income inequalities," Research in Economics, Elsevier, vol. 69(3), pages 439-452.
    2. 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.
    3. Alesina, Alberto & Passarelli, Francesco, 2014. "Regulation versus taxation," Journal of Public Economics, Elsevier, vol. 110(C), pages 147-156.
    4. 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.
    5. Russo, Antonio, 2013. "Voting on road congestion policy," Regional Science and Urban Economics, Elsevier, vol. 43(5), pages 707-724.
    6. Bellani, Luna & Fabella, Vigile Marie & Scervini, Francesco, 2020. "Strategic Compromise, Policy Bundling and Interest Group Power," IZA Discussion Papers 13924, IZA Network @ LISER.
    7. Borissov, Kirill & Pakhnin, Mikhail & Puppe, Clemens, 2017. "On discounting and voting in a simple growth model," European Economic Review, Elsevier, vol. 94(C), pages 185-204.
    8. Hayashi, Takashi & Lombardi, Michele, 2019. "One-step-ahead implementation," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 110-126.
    9. Carlos Bethencourt & Lars Kunze, 2015. "The political economics of redistribution, inequality and tax avoidance," Public Choice, Springer, vol. 163(3), pages 267-287, June.
    10. Dotti, Valerio, 2020. "Income inequality, size of government, and tax progressivity: A positive theory," European Economic Review, Elsevier, vol. 121(C).
    11. 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.
    12. Bellani, Luna & Scervini, Francesco, 2015. "Heterogeneous preferences and in-kind redistribution: Theory and evidence," European Economic Review, Elsevier, vol. 78(C), pages 196-219.
    13. Mikhail Pakhnin, 2023. "Collective choice with heterogeneous time preferences," Journal of Economic Surveys, Wiley Blackwell, vol. 37(3), pages 715-746, July.
    14. 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).
    15. Masciandaro, Donato & Passarelli, Francesco, 2013. "Financial systemic risk: Taxation or regulation?," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 587-596.
    16. 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.
    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.

    More about this item

    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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