Multidimension: a dimensionality extension of simple games

In voting theory and social choice theory, decision systems can be represented as simple games, i.e., cooperative games defined through their players or voters and their set of winning coalitions. The weighted voting games form a well-known strict subclass of simple games, where each player has a vo...

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Autores: Molinero Albareda, Xavier|||0000-0002-5203-4347, Riquelme Csori, Fabian Rolando|||0000-0003-4491-0148, Roura Ferret, Salvador|||0000-0003-4394-5939, Serna Iglesias, María José|||0000-0001-9729-8648
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/398135
Acceso en línea:https://hdl.handle.net/2117/398135
https://dx.doi.org/10.1007/s40314-023-02471-y
Access Level:acceso abierto
Palabra clave:Voting -- Mathematical models
Game theory
Weighted voting games
Dimensionality
Codimensionality
Canonical minimum representation
Vot -- Models matemàtics
Jocs, Teoria de
Classificació AMS::91 Game theory, economics, social and behavioral sciences
Classificació AMS::90 Operations research, mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
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spelling Multidimension: a dimensionality extension of simple gamesMolinero Albareda, Xavier|||0000-0002-5203-4347Riquelme Csori, Fabian Rolando|||0000-0003-4491-0148Roura Ferret, Salvador|||0000-0003-4394-5939Serna Iglesias, María José|||0000-0001-9729-8648Voting -- Mathematical modelsGame theoryGame theoryWeighted voting gamesDimensionalityCodimensionalityCanonical minimum representationVot -- Models matemàticsJocs, Teoria deClassificació AMS::91 Game theory, economics, social and behavioral sciencesClassificació AMS::90 Operations research, mathematical programmingÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocsIn voting theory and social choice theory, decision systems can be represented as simple games, i.e., cooperative games defined through their players or voters and their set of winning coalitions. The weighted voting games form a well-known strict subclass of simple games, where each player has a voting weight so that a coalition wins if the sum of weights of their members exceeds a given quota. Since the number of winning coalitions can be exponential in the number of players, simple games can be represented much more compactly as intersections or unions of weighted voting games. A simple game’s dimension (codimension) is the minimum number of weighted voting games such that their intersection (union) is the given game. It is known there are voting systems with a high (co)dimension. This work introduces the multidimension as the minimum size of an expression with intersections and unions on weighted voting games necessary to obtain the considered simple game. We generalize this notion to subclasses of weighted voting games and analyze the generative properties of these subclasses. We also characterize the simple games with finite generalized multidimension over the set of weighted voting games without dummy players. We provide a comprehensive classification for simple games up to a certain number of players. These results complement similar classification results for generalized (co)dimensions. Our results show how generalized multidimension allows representing more simple games and more compactly, even for a small number of players and for subclasses."Xavier Molinero was partially supported by the Spanish Ministry of Economy and Competitiveness (MINECO) and the European Union (FEDER funds) [PID2019-104987GB-I00, JUVOCO]. Fabián Riquelme was supported by the Fondecyt de Iniciación 11200113 from ANID, Chile. Maria Serna was partially supported by the Spanish Agencia Estatal de Investigación [PID-2020-112581GB-C21, MOTION]. Xavier Molinero, Salvador Roura, and Maria Serna were also partially supported by the Catalan government [2021 SGR 01419 ALBCOM]"Peer ReviewedSpringer20232023-10-2020232023-12-15journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/398135https://dx.doi.org/10.1007/s40314-023-02471-yreponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-104987GB-I00 JUEGOS DE VOTACION Y COOPERACION CON APLICACIONES A LAS REDES SOCIALES Y A LAS CIENCIAS POLITICASAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-112581GB-C21 MODELOS Y TECNICAS PARA EL PROCESAMIENTO DE INFORMACION A GRAN ESCALA -- BARCELONAopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3981352026-05-27T15:37:01Z
dc.title.none.fl_str_mv Multidimension: a dimensionality extension of simple games
title Multidimension: a dimensionality extension of simple games
spellingShingle Multidimension: a dimensionality extension of simple games
Molinero Albareda, Xavier|||0000-0002-5203-4347
Voting -- Mathematical models
Game theory
Game theory
Weighted voting games
Dimensionality
Codimensionality
Canonical minimum representation
Vot -- Models matemàtics
Jocs, Teoria de
Classificació AMS::91 Game theory, economics, social and behavioral sciences
Classificació AMS::90 Operations research, mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
title_short Multidimension: a dimensionality extension of simple games
title_full Multidimension: a dimensionality extension of simple games
title_fullStr Multidimension: a dimensionality extension of simple games
title_full_unstemmed Multidimension: a dimensionality extension of simple games
title_sort Multidimension: a dimensionality extension of simple games
dc.creator.none.fl_str_mv Molinero Albareda, Xavier|||0000-0002-5203-4347
Riquelme Csori, Fabian Rolando|||0000-0003-4491-0148
Roura Ferret, Salvador|||0000-0003-4394-5939
Serna Iglesias, María José|||0000-0001-9729-8648
author Molinero Albareda, Xavier|||0000-0002-5203-4347
author_facet Molinero Albareda, Xavier|||0000-0002-5203-4347
Riquelme Csori, Fabian Rolando|||0000-0003-4491-0148
Roura Ferret, Salvador|||0000-0003-4394-5939
Serna Iglesias, María José|||0000-0001-9729-8648
author_role author
author2 Riquelme Csori, Fabian Rolando|||0000-0003-4491-0148
Roura Ferret, Salvador|||0000-0003-4394-5939
Serna Iglesias, María José|||0000-0001-9729-8648
author2_role author
author
author
dc.subject.none.fl_str_mv Voting -- Mathematical models
Game theory
Game theory
Weighted voting games
Dimensionality
Codimensionality
Canonical minimum representation
Vot -- Models matemàtics
Jocs, Teoria de
Classificació AMS::91 Game theory, economics, social and behavioral sciences
Classificació AMS::90 Operations research, mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
topic Voting -- Mathematical models
Game theory
Game theory
Weighted voting games
Dimensionality
Codimensionality
Canonical minimum representation
Vot -- Models matemàtics
Jocs, Teoria de
Classificació AMS::91 Game theory, economics, social and behavioral sciences
Classificació AMS::90 Operations research, mathematical programming
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
description In voting theory and social choice theory, decision systems can be represented as simple games, i.e., cooperative games defined through their players or voters and their set of winning coalitions. The weighted voting games form a well-known strict subclass of simple games, where each player has a voting weight so that a coalition wins if the sum of weights of their members exceeds a given quota. Since the number of winning coalitions can be exponential in the number of players, simple games can be represented much more compactly as intersections or unions of weighted voting games. A simple game’s dimension (codimension) is the minimum number of weighted voting games such that their intersection (union) is the given game. It is known there are voting systems with a high (co)dimension. This work introduces the multidimension as the minimum size of an expression with intersections and unions on weighted voting games necessary to obtain the considered simple game. We generalize this notion to subclasses of weighted voting games and analyze the generative properties of these subclasses. We also characterize the simple games with finite generalized multidimension over the set of weighted voting games without dummy players. We provide a comprehensive classification for simple games up to a certain number of players. These results complement similar classification results for generalized (co)dimensions. Our results show how generalized multidimension allows representing more simple games and more compactly, even for a small number of players and for subclasses.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-10-20
2023
2023-12-15
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/398135
https://dx.doi.org/10.1007/s40314-023-02471-y
url https://hdl.handle.net/2117/398135
https://dx.doi.org/10.1007/s40314-023-02471-y
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-104987GB-I00 JUEGOS DE VOTACION Y COOPERACION CON APLICACIONES A LAS REDES SOCIALES Y A LAS CIENCIAS POLITICAS
Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-112581GB-C21 MODELOS Y TECNICAS PARA EL PROCESAMIENTO DE INFORMACION A GRAN ESCALA -- BARCELONA
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
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