Academic Journal
Multidimension: a dimensionality extension of simple games
| Τίτλος: | Multidimension: a dimensionality extension of simple games |
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| Συγγραφείς: | Xavier Molinero, Fabián Riquelme, Salvador Roura, Maria Serna |
| Συνεισφορές: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. Departament de Ciències de la Computació, Universitat Politècnica de Catalunya. ALBCOM - Algorísmia, Bioinformàtica, Complexitat i Mètodes Formals |
| Πηγή: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Στοιχεία εκδότη: | Springer Science and Business Media LLC, 2023. |
| Έτος έκδοσης: | 2023 |
| Θεματικοί όροι: | Classificació AMS::90 Operations research, Teoria de, social and behavioral sciences, Classificació AMS::90 Operations research, mathematical programming, 0211 other engineering and technologies, Classificació AMS::91 Game theory, Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs, economics, 0102 computer and information sciences, 02 engineering and technology, Jocs, 16. Peace & justice, Codimensionality, 01 natural sciences, Classificació AMS::91 Game theory, economics, social and behavioral sciences, Weighted voting games, Dimensionality, Canonical minimum representation, Vot -- Models matemàtics, Voting -- Mathematical models, Jocs, Teoria de, mathematical programming, Game theory |
| Περιγραφή: | 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. |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| ISSN: | 1807-0302 2238-3603 |
| DOI: | 10.1007/s40314-023-02471-y |
| Rights: | CC BY |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....5b6a8b9e3a27d9c8bba51871787fda64 |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 18070302 22383603 |
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| DOI: | 10.1007/s40314-023-02471-y |