Enumeration of weighted games with minimum and an analysis of voting power for bipartite complete games with minimum
This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class as well. Second, we focus on the special case of bipartite c...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2014 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/25089 |
| Acesso em linha: | https://hdl.handle.net/2117/25089 https://dx.doi.org/10.1007/s10479-013-1348-x |
| Access Level: | Acceso aberto |
| Palavra-chave: | Voting--Mathematical models Game theory Simple game Weighted and complete games Enumerations Shapley-Shubik power index Banzhaf power indices Ordinal equivalence Europena Union Dimension Semivalues Council Indexes System Vot -- Models matemàtics Jocs, Teoria de Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory Classificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs |
| Resumo: | This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class as well. Second, we focus on the special case of bipartite complete games with minimum, and we compare and rank these games according to the behavior of some efficient power indices of players of type 1 (or of type 2). The main result of this second part establishes all allowable rankings of these games when the Shapley-Shubik power index is used on players of type 1. |
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