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Using the multilinear extension to study some probabilistic power indices
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 |
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