Annals of Operations Research

, Volume 196, Issue 1, pp 361–369 | Cite as

On minimum sum representations for weighted voting games

Article

Abstract

A proposal in a weighted voting game is accepted if the sum of the (non-negative) weights of the “yea” voters is at least as large as a given quota. Several authors have considered representations of weighted voting games with minimum sum, where the weights and the quota are restricted to be integers. In Freixas and Molinero (Ann. Oper. Res. 166:243–260, 2009) the authors have classified all weighted voting games without a unique minimum sum representation for up to 8 voters. Here we exhaustively classify all weighted voting games consisting of 9 voters which do not admit a unique minimum sum integer weight representation.

Keywords

Simple games Weighted voting games Minimum realizations Realizations with minimum sum 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Physics, and Computer ScienceUniversity of BayreuthBayreuthGermany

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