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Multiparty Equilibria under Proportional Representation

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  • Greenberg, Joseph
  • Weber, Shlomo

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.

Suggested Citation

  • Greenberg, Joseph & Weber, Shlomo, 1985. "Multiparty Equilibria under Proportional Representation," American Political Science Review, Cambridge University Press, vol. 79(3), pages 693-703, September.
    • Handle: RePEc:cup:apsrev:v:79:y:1985:i:03:p:693-703_22
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    Cited by:

    1. Maria Gallego & David Scoones, 2011. "Intergovernmental negotiation, willingness to compromise, and voter preference reversals," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(3), pages 591-610, April.
    2. James M. Snyder, 1994. "Safe Seats, Marginal Seats, And Party Platforms: The Logic Of Platform Differentiation," Economics and Politics, Wiley Blackwell, vol. 6(3), pages 201-213, November.
    3. Alexander Shapoval & Shlomo Weber & Alexei Zakharov, 2019. "Valence influence in electoral competition with rank objectives," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 713-753, September.
    4. William Roberts Clark & Matt Golder & Sona Nadenichek Golder, 2002. "Fiscal Policy and the Democratic Process in the European Union," European Union Politics, , vol. 3(2), pages 205-230, June.
    5. Steven J. Brams & Michael A. Jones & D. Marc Kilgour, 2002. "Single-Peakedness and Disconnected Coalitions," Journal of Theoretical Politics, , vol. 14(3), pages 359-383, July.

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