On minimal integer representations of weighted games

Details On minimal integer representations of weighted games On minimal integer representations of weighted games

2011-03-04

arxiv.org/abs/1103.0868v1

Mathematics

Combinatorics

22 pages

Scientific paper

We study minimum integer representations for the weights of weighted games, which is linked with some solution concepts in game theory. Closing some gaps in the existing literature we prove that each weighted game with two types of voters admits a unique minimum integer presentation and give examples for more than two types of voters without a minimum integer representation. We characterize the possible weights in minimum integer representations and give examples for at least four types of voters without minimum integer representations preserving types.

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