Average Weights and Power in Weighted Voting Games

05/10/2019

∙

by   Daria Boratyn, et al.

∙

0

∙

share

We investigate a class of weighted voting games for which weights are randomly distributed over the unit 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 Banzhaf power index and the quota for the uniform measure on the simplex.