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

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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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  • 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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    4. 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.
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    8. Bellani, Luna & Scervini, Francesco, 2015. "Heterogeneous preferences and in-kind redistribution: Theory and evidence," European Economic Review, Elsevier, vol. 78(C), pages 196-219.
    9. Alesina, Alberto & Passarelli, Francesco, 2014. "Regulation versus taxation," Journal of Public Economics, Elsevier, vol. 110(C), pages 147-156.
    10. Mikhail Pakhnin, 2021. "Collective Choice with Heterogeneous Time Preferences," CESifo Working Paper Series 9141, CESifo.
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    14. 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).
    15. 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.
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    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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