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

46 Pages Posted: 20 Jan 2010

See all articles by Philippe De Donder

Philippe De Donder

University of Toulouse 1 - Toulouse School of Economics (TSE)

Michel Le Breton

University of Toulouse I - GREMAQ-IDEI

Eugenio Peluso

University of Verona - Department of Economics

Date Written: January 2010

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.

Keywords: one-sided separability, single crossing condition, Unidimensional and bidimensional type space

JEL Classification: D72, H41

Suggested Citation

De Donder, Philippe and Le Breton, Michel and Peluso, Eugenio, Majority Voting in Multidimensional Policy Spaces: Kramer-Shepsle Versus Stackelberg (January 2010). CEPR Discussion Paper No. DP7646, Available at SSRN: https://ssrn.com/abstract=1539318

Philippe De Donder (Contact Author)

University of Toulouse 1 - Toulouse School of Economics (TSE) ( email )

Place Anatole-France
Toulouse Cedex, F-31042
France

Michel Le Breton

University of Toulouse I - GREMAQ-IDEI ( email )

Manufacture des Tabacs
21 Allees de Brienne
Toulouse, 31000
France

Eugenio Peluso

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

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