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dc.contributor.authorFreixas Bosch, Josep
dc.contributor.authorKurz, Sascha
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2016-05-10T14:22:58Z
dc.date.available2019-07-01T08:05:59Z
dc.date.issued2016-06-01
dc.identifier.citationFreixas, J., Kurz, S. The cost of getting local monotonicity. "European journal of operational research", 01 Juny 2016, vol. 251, núm. 2, p. 600-612.
dc.identifier.issn0377-2217
dc.identifier.urihttp://hdl.handle.net/2117/86881
dc.description.abstractCommittees with yes-no-decisions are commonly modeled as simple games and the ability of a member to influence the group decision is measured by so-called power indices. For a weighted game we say that a power index satisfies local monotonicity if a player who controls a large share of the total weight vote does not have less power than a player with a smaller voting weight. In (Holler, 1982) Manfred Holler introduced the Public Good index. In its unnormalized version, i.e., the raw measure, it counts the number of times that a player belongs to a minimal winning coalition. Unlike the Banzhaf index, it does not count the remaining winning coalitions in which the player is crucial. Holler noticed that his index does not satisfy local monotonicity, a fact that can be seen either as a major drawback (Felsenthal & Machover, 1998, 221 ff.)or as an advantage (Holler & Napel 2004). In this paper we consider a convex combination of the two indices and require the validity of local monotonicity. We prove that the cost of obtaining it is high, i.e., the achievable new indices satisfying local monotonicity are closer to the Banzhaf index than to the Public Good index. All these achievable new indices are more solidary than the Banzhaf index, which makes them as very suitable candidates to divide a public good. As a generalization we consider convex combinations of either: the Shift index, the Public Good index, and the Banzhaf index, or alternatively: the Shift Deegan-Packel, Deegan-Packel, and Johnston indices.
dc.format.extent13 p.
dc.language.isoeng
dc.publisherElsevier
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
dc.subject.lcshVoting--Mathematical models
dc.subject.lcshGame theory
dc.subject.otherDesign of power indices
dc.subject.otherLocal monotonicity
dc.subject.otherPublic Good index
dc.subject.otherSimple games
dc.subject.otherWeighted games
dc.titleThe cost of getting local monotonicity
dc.typeArticle
dc.subject.lemacVot -- Models matemàtics
dc.subject.lemacJocs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs
dc.identifier.doi10.1016/j.ejor.2015.11.030
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory
dc.subject.amsClassificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics
dc.rights.accessOpen Access
local.identifier.drac17838621
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO//MTM2012-34426/ES/TEORIA DE JUEGOS: FUNDAMENTOS MATEMATICOS Y APLICACIONES/
local.citation.authorFreixas, J.; Kurz, S.
local.citation.publicationNameEuropean journal of operational research
local.citation.volume251
local.citation.number2
local.citation.startingPage600
local.citation.endingPage612


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