Average weights and power in weighted voting games

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

Mathematical Social Sciences, 2020, vol. 108, issue C, 90-99

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.

Keywords: Random weighted voting games; Voting power; Penrose–Banzhaf index; Coleman efficiency index; Order statistics (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:108:y:2020:i:c:p:90-99

DOI: 10.1016/j.mathsocsci.2020.04.002

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