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Title:
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Minimal representations for majority games
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Author:
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Freixas Bosch, Josep; Molinero Albareda, Xavier; Roura Ferret, Salvador
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. Departament de Llenguatges i Sistemes Informàtics; Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs; Universitat Politècnica de Catalunya. ALBCOM - Algorismia, Bioinformàtica, Complexitat i Mètodes Formals |
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Abstract:
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This paper presents some new results about majority games. Isbell (1959) was the first to find a majority game without a minimum normalized representation; he needed 12 voters to construct such a game. Since then, it has been an open problem to find the minimum number of voters of a majority game without a minimum normalized representation. Our main new results are: 1. All majority games with less than 9 voters have a minimum representation. 2. For 9 voters there are 14 majority games without a minimum integer representation, but these games admit a minimal normalized integer representation. 3. For 10 voters exist majority games with neither a minimum integer representation nor a minimal normalized integer representation. |
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Subject(s):
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-Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
-Simple games
-Weighted games
-Majority games
-Minimum and minimal weighted representations/realizations
-Computing games |
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Rights:
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Document type:
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Article - Published version
Report |
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