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

Kurz, Sascha, Bounds for the Diameter of the Weight Polytope (August 8, 2018). Available at SSRN: https://ssrn.com/abstract=3228524 or http://dx.doi.org/10.2139/ssrn.3228524

Sascha Kurz (Contact Author)

University of Bayreuth ( email )

Universitätsstr. 30
Lehrstuhl für Wirtschaftsmathematik
Bayreuth, Bavaria D-95440
Germany
+49 921 55 7353 (Phone)
+49 921 55 7352 (Fax)

HOME PAGE: http://www.wm.uni-bayreuth.de/index.php?id=sascha

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