Weighted simple games and the topology of simplicial complexes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912556720848896 |
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| author | Brooks, Anastasia Sarcevic, Franjo Volic, Ismar |
| author_facet | Brooks, Anastasia Sarcevic, Franjo Volic, Ismar |
| contents | We use simplicial complexes to model simple games as well as weighted voting games where certain coalitions are considered impossible. Topological characterizations of various ideas from simple games are provided, as are the expressions for Banzhaf and Shapley-Shubik power indices for weighted games. We calculate the indices in several examples of weighted voting games with unfeasible coalitions, including the U.S. Electoral College and the Parliament of Bosnia-Herzegovina. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_09771 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Weighted simple games and the topology of simplicial complexes Brooks, Anastasia Sarcevic, Franjo Volic, Ismar Physics and Society Combinatorics 91F10, 91B12, 05E45 We use simplicial complexes to model simple games as well as weighted voting games where certain coalitions are considered impossible. Topological characterizations of various ideas from simple games are provided, as are the expressions for Banzhaf and Shapley-Shubik power indices for weighted games. We calculate the indices in several examples of weighted voting games with unfeasible coalitions, including the U.S. Electoral College and the Parliament of Bosnia-Herzegovina. |
| title | Weighted simple games and the topology of simplicial complexes |
| topic | Physics and Society Combinatorics 91F10, 91B12, 05E45 |
| url | https://arxiv.org/abs/2210.09771 |