Dimension of complete simple games with minimum |
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Authors: | Josep Freixas,Marí a Albina Puente |
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Affiliation: | Department of Applied Mathematics III, Engineering School of Manresa, Technical University of Catalonia, Spain |
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Abstract: | Weighted majority games have the property that players are totally ordered by the desirability relation (introduced by Isbell in [J.R. Isbell, A class of majority games, Quarterly Journal of Mathematics, 7 (1956) 183–187]) because weights induce it. Games for which this relation is total are called complete simple games. Taylor and Zwicker proved in [A.D. Taylor, W.S. Zwicker, Weighted voting, multicameral representation, and power, Games and Economic Behavior 5 (1993) 170–181] that every simple game (or monotonic finite hypergraph) can be represented by an intersection of weighted majority games and consider the dimension of a game as the needed minimum number of them to get it. They provide the existence of non-complete simple games of every dimension and left open the problem for complete simple games. |
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Keywords: | Simple games Hypergraphs Boolean algebra Weighted majority games Complete simple games Dimension |
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