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An Application of Power Indices for the Family of Weighted Majority Games in Partition Function Form

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Power and Responsibility

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.

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Notes

  1. 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. 2.

    https://www.primicias.ec/noticias/politica/los-cambios-en-las-bancadas-de-la-asamblea/, last accessed 23/12/2021.

  3. 3.

    https://www.primicias.ec/noticias/politica/bancadas-pierden-miembros-votos-asamblea/, last accessed 23/12/2021.

  4. 4.

    https://www.primicias.ec/noticias/politica/union-unes-pachakutik-debilidad-legislativa-gobierno/, last accessed 23/12/2021.

  5. 5.

    https://www.primicias.ec/noticias/politica/posible-destitucion-lasso-apoyo-asamblea/, last accessed 23/12/2021.

  6. 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.

Author information

Authors and Affiliations

  1. MODESTYA Research Group, Department of Statistics, Mathematical Analysis and Optimisation, Faculty of Sciences, University of Santiago de Compostela, Campus de Lugo, 27002, Lugo, Spain

    J. M. Alonso-Meijide

  2. Departamento de Ciencias Exactas, Universidad de las Fuerzas Armadas ESPE, Sangolquí, Ecuador

    L. M. Armijos-Toro

  3. MODESTYA Research Group, Department of Statistics, Mathematical Analysis and Optimisation, Faculty of Mathematics, University of Santiago de Compostela, Campus Vida, 15782, Santiago de Compostela, Coruna, Spain

    L. M. Armijos-Toro & B. Casas-Méndez

  4. Universidade de Vigo, Departamento de Estatística e Investigación Operativa, 32004, Ourense, Spain

    M. A. Mosquera

  5. CITMAga, 15782, Santiago de Compostela, Coruna, Spain

    J. M. Alonso-Meijide, L. M. Armijos-Toro, B. Casas-Méndez & M. A. Mosquera

Authors
  1. J. M. Alonso-Meijide
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  2. L. M. Armijos-Toro
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  3. B. Casas-Méndez
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  4. M. A. Mosquera
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Corresponding author

Correspondence to J. M. Alonso-Meijide .

Editor information

Editors and Affiliations

  1. Pforzheim University of Applied Sciences, Pforzheim, Germany

    Martin A. Leroch

  2. Kutaisi International University, Kutaisi, Georgia

    Florian Rupp

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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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