# Average Weights and Power in Weighted Voting Games

arXiv: https://arxiv.org/abs/1905.04261 · HTML: https://mlsanity.com/paper/1905.04261/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2019.

## Built on by (most cited first, 1 of 1)

- [Measuring a Priori Voting Power -- Taking Delegations Seriously](https://mlsanity.com/paper/2301.02462/) (2023)

## Abstract (arXiv)

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.