dc.contributor.author Freixas Bosch, Josep dc.contributor.author Pons Vallès, Montserrat dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2017-05-17T14:32:45Z dc.date.available 2018-06-01T00:30:25Z dc.date.issued 2017-05-01 dc.identifier.citation Freixas, J., Pons, M. Using the multilinear extension to study some probabilistic power indices. "Group decision and negotiation", 1 Maig 2017, vol. 26, núm. 3, p. 437-452. dc.identifier.issn 0926-2644 dc.identifier.uri http://hdl.handle.net/2117/104580 dc.description The final publication is available at Springer via http://dx.doi.org/10.1007/s10726-016-9514-6 dc.description.abstract We consider binary voting systems modeled by a simple game, in which voters vote independently of each other, and the probability distribution over coalitions is known. The Owen’s multilinear extension of the simple game is used to improve the use and the computation of three indices defined in this model: the decisiveness index, which is an extension of the Banzhaf index, the success index, which is an extension of the Rae index, and the luckiness index. This approach leads us to prove new properties and inter-relations between these indices. In particular it is proved that the ordinal equivalence between success and decisiveness indices is achieved in any game if and only if the probability distribution is anonymous. In the anonymous case, the egalitarianism of the three indices is compared, and it is also proved that, for these distributions, decisiveness and success indices respect the strength of the seats, whereas luckiness reverses this order. dc.format.extent 16 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 Decision making -- Mathematical models dc.subject.lcsh Voting -- Mathematical models dc.subject.other Game theory dc.subject.other Voting dc.subject.other Simple games dc.subject.other Power indices dc.subject.other Multilinear extension dc.title Using the multilinear extension to study some probabilistic power indices dc.type Article dc.subject.lemac Jocs, Teoria de dc.subject.lemac Decisió, Presa de -- Models matemàtics dc.subject.lemac Vot -- Models matemàtics dc.contributor.group Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs dc.identifier.doi 10.1007/s10726-016-9514-6 dc.description.peerreviewed Peer Reviewed dc.subject.ams Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory dc.relation.publisherversion https://link.springer.com/article/10.1007%2Fs10726-016-9514-6 dc.rights.access Open Access local.identifier.drac 20335255 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 Freixas, J.; Pons, M. local.citation.publicationName Group decision and negotiation local.citation.volume 26 local.citation.number 3 local.citation.startingPage 437 local.citation.endingPage 452
﻿