On $α$-roughly weighted games

Details On $α$-roughly weighted games On $α$-roughly weighted games

2011-12-13

arxiv.org/abs/1112.2861v1

Mathematics

Combinatorics

22 pages, 1 table

Scientific paper

Very recently Gvozdeva, Hemaspaandra, and Slinko (2011) have introduced three hierarchies for simple games in order to measure the distance of a given simple game to the class of weighted voting games or roughly weighted voting games. Their third class $\mathcal{C}_\alpha$ consists of all simple games permitting a weighted representation such that each winning coalition has a weight of at least 1 and each losing coalition a weight of at most $\alpha$. We continue their work and contribute some new results on the possible values of $\alpha$ for a given number of voters.

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