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Voting Power and Proportional Representation of Voters

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  • Yair Tauman

    ()
    (Department of Economics, Stony Brook University)

  • Artyom Jelnov

    ()
    (The Faculty of Management, Tel Aviv University, Israel)

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    Abstract

    Our paper provides a justi cation for the proportional representative (PR) election system for politically diversi ed societies. We employ the Shapley value concept to measure the political power of parties in a parliament. We prove that for the PR system if parties' size add up to 1 and is uniformly distributed, the expected ratio of a party size to its political power converges to 1, and the variance decreases to 0 as the number of parties increases. The rate of convergence is high. An empirical evidence from the Netherlands elections supports our result. Using the Shapley-Owen index we obtain similar result (this time numerically only) for a voting model that takes into account ideological differences between parties and voters.

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    File URL: http://www.sunysb.edu/economics/research/papers/2012/Jelnov-Tauman.pdf
    File Function: First version, 2012
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    Bibliographic Info

    Paper provided by Stony Brook University, Department of Economics in its series Department of Economics Working Papers with number 12-04.

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    Date of creation: Aug 2012
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    Handle: RePEc:nys:sunysb:12-04

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    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
    2. Dubey, Pradeep & Einy, Ezra & Haimanko, Ori, 2005. "Compound voting and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 51(1), pages 20-30, April.
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