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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The counting vector of a simple game


Author: Eitan Lapidot
Journal: Proc. Amer. Math. Soc. 31 (1972), 228-231
DOI: https://doi.org/10.1090/S0002-9939-1972-0287916-7
MathSciNet review: 0287916
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Abstract: The counting vector of a simple game is the vector $ f = (f(1),f(2), \cdots ,f(n))$ where $ f(i)$ is the number of winning coalitions containing the player $ i$. In this paper, we show that the counting vector of a weighted majority game determines the game uniquely. With the aid of the counting vector we find an upper bound on the number of weighted majority games.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0287916-7
Keywords: Simple games, weighted majority game, counting vector, desirability relation, symmetric players
Article copyright: © Copyright 1972 American Mathematical Society