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Minimal representations for majority games
dc.contributor.author | Freixas Bosch, Josep |
dc.contributor.author | Molinero Albareda, Xavier |
dc.contributor.author | Roura Ferret, Salvador |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Llenguatges i Sistemes Informàtics |
dc.date.accessioned | 2016-04-27T07:22:54Z |
dc.date.available | 2016-04-27T07:22:54Z |
dc.date.issued | 2007-02 |
dc.identifier.citation | Freixas, J., Molinero, X., Roura, S. "Minimal representations for majority games". 2007. |
dc.identifier.uri | http://hdl.handle.net/2117/86215 |
dc.description.abstract | 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. |
dc.format.extent | 11 p. |
dc.language.iso | eng |
dc.relation.ispartofseries | LSI-07-11-R |
dc.subject | Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
dc.subject.other | Simple games |
dc.subject.other | Weighted games |
dc.subject.other | Majority games |
dc.subject.other | Minimum and minimal weighted representations/realizations |
dc.subject.other | Computing games |
dc.title | Minimal representations for majority games |
dc.type | External research report |
dc.contributor.group | Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs |
dc.contributor.group | Universitat Politècnica de Catalunya. ALBCOM - Algorismia, Bioinformàtica, Complexitat i Mètodes Formals |
dc.rights.access | Open Access |
local.identifier.drac | 604140 |
dc.description.version | Postprint (published version) |
local.citation.author | Freixas, J.; Molinero, X.; Roura, S. |
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