Technical Report 1905.04261 [cs.GT], May, 2019.

Paper abstract bibtex

Paper abstract bibtex

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.

@techreport{BoratynEtAl19, type = {{{arXiv}}}, title = {Average {{Weights}} and {{Power}} in {{Weighted Voting Games}}}, author = {Boratyn, Daria and Kirsch, Werner and Słomczyński, Wojciech and Stolicki, Dariusz and Życzkowski, Karol}, year = {2019}, month = may, number = {1905.04261 [cs.GT]}, eprint = {1905.04261}, eprinttype = {arxiv}, url = {http://arxiv.org/abs/1905.04261}, urldate = {2019-09-05}, abstract = {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.}, archiveprefix = {arXiv}, keywords = {2010: Primary 91A12; Secondary 60E05; 60E10,Computer Science - Computer Science and Game Theory,Mathematics - Probability,Physics - Physics and Society} }

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