Multiparty Equilibria under Proportional Representation

Joseph Greenberg and Shlomo Weber

American Political Science Review, 1985, vol. 79, issue 3, 693-703

Abstract: The purpose of this article is to define and to prove formally the existence of an equilibrium under proportional representation, as well as partially to characterize it. Specifically, let m be the quota that represents the minimal number of voters necessary for a candidate to be elected. We show that there is a set of elected candidates, each choosing an alternative and each receiving at least m votes, such that no other potential candidate, by offering an additional alternative, can secure at least m votes for himself. We then investigate the structure, at equilibrium, of the set of individuals who support a given candidate, as well as study stability properties of the equilibrium. We also provide necessary and sufficient conditions for the equilibrium to consist of a single candidate, thus generalizing Black's median-voter result.

Date: 1985
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