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Título: | Generating functions of weighted voting games, MacMahon’s Partition Analysis, and Clifford algebras. |
Autor(es): | Francisco Neto, Antônio |
Palavras-chave: | Banzhaf power index Shapley-Shubik power index Coalitional power indices Coalition configuration Linear diophantine system |
Data do documento: | 2019 |
Referência: | FRANCISCO NETO, A. Generating functions of weighted voting games, MacMahon’s Partition Analysis, and Clifford algebras. Mathematics of Operations Research, v. 44, n. 1, fev. 2019. Disponível em: <https://pubsonline.informs.org/doi/10.1287/moor.2017.0915>. Acesso em: 10 mar. 2020. |
Resumo: | MacMahon’s Partition Analysis (MPA) is a combinatorial tool used in partition analysis to describe the solutions of a linear diophantine system. We show that MPA is useful in the context of weighted voting games. We introduce a new generalized generating function that gives, as special cases, extensions of the generating functions of the Banzhaf, Shapley-Shubik, Banzhaf-Owen, symmetric coalitional Banzhaf, and Owen power indices. Our extensions involve any coalition formation related to a linear diophantine system and multiple voting games. In addition, we show that a combination of ideas from MPA and Clifford algebras is useful in constructing generating functions for coalition configuration power indices. Finally, a brief account on how to design voting systems via MPA is advanced. More precisely, we obtain new generating functions that give, for fixed coalitions, all the distribution of weights of the players of the voting game such that a given player swings or not. |
URI: | http://www.repositorio.ufop.br/handle/123456789/12739 |
Link para o artigo: | https://pubsonline.informs.org/doi/10.1287/moor.2017.0915 |
DOI: | https://doi.org/10.1287/moor.2017.0915 |
ISSN: | 1526-5471 |
Aparece nas coleções: | DEPRO - Artigos publicados em periódicos |
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ARTIGO_GeneratingFunctionsWeighted.pdf Restricted Access | 491,34 kB | Adobe PDF | Visualizar/Abrir |
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