Average Weights and Power in Weighted Voting Games
Abstract
We investigate a class of weighted voting games for which weights are randomly distributed over the standard probability simplex. We provide closeformed 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 PenroseBanzhaf 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.04261
 Bibcode:
 2019arXiv190504261B
 Keywords:

 Computer Science  Computer Science and Game Theory;
 Mathematics  Probability;
 Physics  Physics and Society;
 Primary 91A12;
 Secondary 60E05;
 60E10
 EPrint:
 12 pages, 7 figures