Bounds for the Diameter of the Weight Polytope
16 Pages Posted: 20 Aug 2018 Last revised: 6 Jul 2019
Date Written: August 8, 2018
Abstract
A weighted game or a threshold function in general admits different weighted representations even if the sum of non-negative weights is fixed to one. Here we study bounds for the diameter of the corresponding weight polytope. It turns out that the diameter can be upper bounded in terms of the maximum weight and the quota or threshold. We apply those results to approximation results between power distributions, given by power indices, and weights.
Keywords: weighted game, threshold function, weighted representations, weight polytope, diameter, power indices
JEL Classification: C71, D72
Suggested Citation: Suggested Citation