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Voting power and proportional representation of voters

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  • Artyom Jelnov
  • Yair Tauman

Abstract

We prove that for the proportional representative election system if parties’ sizes are uniformly distributed on the simplex, the expected ratio of a party size to its political power, measured by the Shapley–Shubik index, converges to $$1$$ 1 , as the number $$n$$ n of parties increases indefinitely. The rate of convergence is high and it is of the magnitude of $$\frac{1}{n}$$ 1 n . Empirical evidence from the Netherlands elections supports our result. A comparison with the Banzhaf index is provided. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Artyom Jelnov & Yair Tauman, 2014. "Voting power and proportional representation of voters," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 747-766, November.
  • Handle: RePEc:spr:jogath:v:43:y:2014:i:4:p:747-766
    DOI: 10.1007/s00182-013-0400-z
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    Cited by:

    1. Boratyn, Daria & Kirsch, Werner & Słomczyński, Wojciech & Stolicki, Dariusz & Życzkowski, Karol, 2020. "Average weights and power in weighted voting games," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 90-99.
    2. Kurz, Sascha & Maaser, Nicola & Napel, Stefan, 2018. "Fair representation and a linear Shapley rule," Games and Economic Behavior, Elsevier, vol. 108(C), pages 152-161.
    3. 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.
    4. Xavier Molinero & Maria Serna & Marc Taberner-Ortiz, 2021. "On Weights and Quotas for Weighted Majority Voting Games," Games, MDPI, vol. 12(4), pages 1-25, December.

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