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Average weights and power in weighted voting games

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  • Boratyn, Daria
  • Kirsch, Werner
  • Słomczyński, Wojciech
  • Stolicki, Dariusz
  • Życzkowski, Karol

Abstract

We investigate a class of weighted voting games for which weights are randomly distributed over the standard probability simplex. We provide close-formed formulae for the expectation and density of the distribution of weight of the k-th largest player under the uniform distribution. We analyze the average voting power of the k-th largest player and its dependence on the quota, obtaining analytical and numerical results for small values of n and a general theorem about the functional form of the relation between the average Penrose–Banzhaf power index and the quota for the uniform measure on the simplex. We also analyze the power of a collectivity to act (Coleman efficiency index) of random weighted voting games, obtaining analytical upper bounds therefor.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matsoc:v:108:y:2020:i:c:p:90-99
    DOI: 10.1016/j.mathsocsci.2020.04.002
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    References listed on IDEAS

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    1. 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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