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On the construction of high dimensional simple games
dc.contributor.author | Olsen, Martin |
dc.contributor.author | Kurz, Sascha |
dc.contributor.author | Molinero Albareda, Xavier |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2016-12-01T19:18:00Z |
dc.date.available | 2016-12-01T19:18:00Z |
dc.date.issued | 2016 |
dc.identifier.citation | Olsen, M., Kurz, S., Molinero, X. On the construction of high dimensional simple games. A: European Conference on Artificial Intelligence. "ECAI 2016: 22nd European Conference on Artificial Intelligence: 29 August–2 September 2016, The Hague, The Netherlands: proceedings". New York: IOS Press, 2016, p. 880-885. |
dc.identifier.isbn | 978-1-61499-672-9 |
dc.identifier.uri | http://hdl.handle.net/2117/97663 |
dc.description.abstract | Voting is a commonly applied method for the aggregation of the preferences of multiple agents into a joint decision. If preferences are binary, i.e., “yes” and “no”, every voting system can be described by a (monotone) Boolean function : f0; 1gn ! f0; 1g. However, its naive encoding needs 2n bits. The subclass of threshold functions, which is sufficient for homogeneous agents, allows a more succinct representation using n weights and one threshold. For heterogeneous agents one can represent as an intersection of k threshold functions. Taylor and Zwicker have constructed a sequence of examples requiring k 2 n2 ¿1 and provided a construction guaranteeingk ¿ n bn=2c 2 2n¿o(n). The magnitude of the worst case situation was thought to be determined by Elkind et al. in 2008, but the analysis unfortunately turned out to be wrong. Here we uncover a relation to coding theory that allows the determination of the minimum number k for a subclass of voting systems. As an application, we give a construction for k 2n¿o(n), i.e., there is no gain from a representation complexity point of view. |
dc.format.extent | 6 p. |
dc.language.iso | eng |
dc.publisher | IOS Press |
dc.rights.uri | http://creativecommons.org/licenses/by-nc/3.0/es/ |
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 construction of high dimensional simple games |
dc.type | Conference report |
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.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics |
dc.subject.ams | Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory |
dc.subject.ams | Classificació AMS::68 Computer science::68P Theory of data |
dc.rights.access | Open Access |
local.identifier.drac | 19241770 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2015-66818-P/ES/ASPECTOS MATEMATICOS, COMPUTACIONALES Y SOCIALES EN CONTEXTOS DE VOTACION Y DE COOPERACION./ |
local.citation.author | Olsen, M.; Kurz, S.; Molinero, X. |
local.citation.contributor | European Conference on Artificial Intelligence |
local.citation.pubplace | New York |
local.citation.publicationName | ECAI 2016: 22nd European Conference on Artificial Intelligence: 29 August–2 September 2016, The Hague, The Netherlands: proceedings |
local.citation.startingPage | 880 |
local.citation.endingPage | 885 |