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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)

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.

Suggested Citation

  • Yair Tauman & Artyom Jelnov, 2012. "Voting Power and Proportional Representation of Voters," Department of Economics Working Papers 12-04, Stony Brook University, Department of Economics.
  • Handle: RePEc:nys:sunysb:12-04
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    References listed on IDEAS

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    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    2. Lindner, Ines & Owen, Guillermo, 2007. "Cases where the Penrose limit theorem does not hold," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 232-238, May.
    3. Nicolas Houy & William S. Zwicker, 2013. "The geometry of voting power : weighted voting and hyper-­ellipsoids," Working Papers halshs-00772953, HAL.
    4. Lindner, Ines & Machover, Moshe, 2004. "L.S. Penrose's limit theorem: proof of some special cases," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 37-49, January.
    5. 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.
    6. Chang, Pao-Li & Chua, Vincent C.H. & Machover, Moshe, 2006. "L S Penrose's limit theorem: Tests by simulation," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 90-106, January.
    7. Raphael Debets, 2008. "Performance Budgeting in the Netherlands," OECD Journal on Budgeting, OECD Publishing, vol. 7(4), pages 1-20.
    8. Dan Felsenthal & Moshé Machover, 2005. "Voting power measurement: a story of misreinvention," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 485-506, December.
    9. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
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    Cited by:

    1. Matteo Migheli, 2016. "Measuring Representativeness in Different Electoral Systems, Using Italian and Dutch Data," Group Decision and Negotiation, Springer, vol. 25(4), pages 723-748, July.

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