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Multiparty Equilibria under Proportional Representation

Published online by Cambridge University Press:  01 August 2014

Joseph Greenberg  and
Shlomo Weber
Joseph Greenberg
Affiliation:
University of Haifa
Shlomo Weber
Affiliation:
University of Haifa
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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.

Type
Research Article
Information
American Political Science Review , Volume 79 , Issue 3 , September 1985 , pp. 693 - 703
Copyright
Copyright © American Political Science Association 1985

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References

Black, D. The theory of committees and elections. Cambridge: Cambridge University Press, 1958.Google Scholar
Downs, A. An economic theory of democracy. New York: Harper & Row, 1957.Google Scholar
Hoag, C. & Hallett, G. Proportional representation. New York: Macmillan, 1926.Google Scholar
Wells, H. G. Westminster Gazette, 12 1, 1923.Google Scholar