Working Paper: CEPR ID: DP7646
Authors: 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.
Keywords: one-sided separability; single crossing condition; unidimensional; bidimensional type space
JEL Codes: D72; H41
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| single crossing conditions (C29) | existence of KS equilibrium (C62) |
| single crossing conditions (C29) | uniqueness of KS equilibrium (C62) |
| marginal single crossing condition (D10) | existence of KS solution (C62) |
| marginal single crossing condition (D10) | uniqueness of KS solution (C62) |
| strategic complementarity (D10) | KS equilibrium coincides with ST equilibrium (D50) |
| bidimensional type space (C39) | existence of KS equilibria (C62) |
| bidimensional type space (C39) | uniqueness of KS equilibria (C62) |
| voting procedures (D72) | policy outcomes (D78) |