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On the existence of a minimum integer representation for weighted voting systems
dc.contributor.author | Freixas Bosch, Josep |
dc.contributor.author | Molinero Albareda, Xavier |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Llenguatges i Sistemes Informàtics |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III |
dc.date.accessioned | 2010-10-06T15:56:39Z |
dc.date.available | 2010-10-06T15:56:39Z |
dc.date.created | 2009-02 |
dc.date.issued | 2009-02 |
dc.identifier.citation | Freixas, J.; Molinero, X. On the existence of a minimum integer representation for weighted voting systems. "Annals of operations research", Febrer 2009, vol. 166, núm. 1, p. 243-260. |
dc.identifier.issn | 0254-5330 |
dc.identifier.uri | http://hdl.handle.net/2117/9470 |
dc.description.abstract | 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 |
dc.format.extent | 18 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs |
dc.subject.lcsh | Game theory |
dc.subject.lcsh | Voting--Mathematical models |
dc.title | On the existence of a minimum integer representation for weighted voting systems |
dc.type | Article |
dc.subject.lemac | Jocs, Teoria de |
dc.subject.lemac | Vot -- Models matemàtics |
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.identifier.doi | 10.1007/s10479-008-0422-2 |
dc.subject.ams | Classificació AMS::91 Game theory, economics, social and behavioral sciences |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 758410 |
dc.description.version | Postprint (published version) |
local.citation.author | Freixas, J.; Molinero, X. |
local.citation.publicationName | Annals of operations research |
local.citation.volume | 166 |
local.citation.number | 1 |
local.citation.startingPage | 243 |
local.citation.endingPage | 260 |
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