De Donder, Philippe, Le Breton, Michel and Peluso, Eugenio (2010) Majority Voting in Multidimensional Policy Spaces: Kramer-Shepsle versus Stackelberg. IDEI Working Paper, n. 593, Toulouse

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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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• Majority Voting in Multidimensional Policy Spaces. (deposited 14 Jun 2016 07:46) [Currently Displayed]
  • Majority Voting in Multidimensional Policy Spaces: Kramer-Shepsle versus Stackelberg. (deposited 09 Jul 2014 17:32)