Title:
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On the existence of a minimum integer representation for weighted voting systems
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Author:
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Freixas Bosch, Josep; Molinero Albareda, Xavier
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Llenguatges i Sistemes Informàtics; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs; Universitat Politècnica de Catalunya. ALBCOM - Algorismia, Bioinformàtica, Complexitat i Mètodes Formals |
Abstract:
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A basic problem in the theory of simple games and other fields is to study whether
a simple game (Boolean function) is weighted (linearly separable). A second related problem
consists in studying whether a weighted game has a minimum integer realization. In this
paper we simultaneously analyze both problems by using linear programming.
For less than 9 voters, we find that there are 154 weighted games without minimum
integer realization, but all of them have minimum normalized realization. Isbell in 1958 was
the first to find a weighted game without a minimum normalized realization, he needed to
consider 12 voters to construct a game with such a property. The main result of this work
proves the existence of weighted games with this property with less than 12 voters |
Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs -Game theory -Voting--Mathematical models -Jocs, Teoria de -Vot -- Models matemàtics -Classificació AMS::91 Game theory, economics, social and behavioral sciences |
Rights:
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Document type:
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Article - Published version Article |
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