Abstract
Based on Holler (1982), Colomer and Martínez (1995), and Armijos-Toro et al. (2021), we propose two power indices to measure the influence of the players in these classes of weighted majority games in partition function form. We compare the new power indices with their original versions on the class of games in characteristic function form. Finally, we use both new power indices and the two power indices for games in partition function form studied in Alonso-Meijide et al. (2017) to study the distribution of power in the National Assembly of Ecuador that emerged after the elections of February 7, 2021.
Keywords
- Weighted majority games
- Partition function form games
- Minimal winning embedded coalitions
- Deegan–Packel power index
- Colomer–Martínez power index
- Public Good power index
Math. Subj. Class. (2020)
- 91A12
- 91A80
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- 1.
A proper subset, \((T;\textsf{Q})\sqsubset (S;\textsf{P})\), is a subset \((T;\textsf{Q})\sqsubseteq (S;\textsf{P})\) satisfying \((T;\textsf{Q})\ne (S;\textsf{P})\).
- 2.
https://www.primicias.ec/noticias/politica/los-cambios-en-las-bancadas-de-la-asamblea/, last accessed 23/12/2021.
- 3.
https://www.primicias.ec/noticias/politica/bancadas-pierden-miembros-votos-asamblea/, last accessed 23/12/2021.
- 4.
https://www.primicias.ec/noticias/politica/union-unes-pachakutik-debilidad-legislativa-gobierno/, last accessed 23/12/2021.
- 5.
https://www.primicias.ec/noticias/politica/posible-destitucion-lasso-apoyo-asamblea/, last accessed 23/12/2021.
- 6.
https://www.primicias.ec/noticias/politica/ruptura-pachakutik-capitulo-bancadas-desgranads/, last accessed 23/12/2021.
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Acknowledgements
We would like to acknowledge the valuable comments of an anonymous referee. This work is part of the R+D+I project grants MTM2017-87197-C3-2-P, MTM2017-87197-C3-3-P, PID2021-124030NB-C32 and PID2021-124030NB-C33, that were funded by MCIN/AEI/10.13039/501100011033/ and by “ERDF A way of making Europe”/EU. This research was also funded by Grupos de Referencia Competitiva ED431C-2020/03 and ED431C-2021/24 from the Consellería de Cultura, Educación e Universidades, Xunta de Galicia.
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Alonso-Meijide, J.M., Armijos-Toro, L.M., Casas-Méndez, B., Mosquera, M.A. (2023). An Application of Power Indices for the Family of Weighted Majority Games in Partition Function Form. In: Leroch, M.A., Rupp, F. (eds) Power and Responsibility. Springer, Cham. https://doi.org/10.1007/978-3-031-23015-8_8
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