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Weighted multiple majority games with unions: Generating functions and applications to the European Union

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  • Alonso-Meijide, J.M.
  • Bilbao, J.M.
  • Casas-Méndez, B.
  • Fernández, J.R.

Abstract

An a priori system of unions or coalition structure is a partition of a finite set of players into disjoint coalitions which have made a prior commitment to cooperate in playing a game. This paper provides "ready-to-apply" procedures based on generating functions that are easily implementable to compute coalitional power indices in weighted multiple majority games. As an application of the proposed procedures, we calculate and compare coalitional power indices under the decision rules prescribed by the Treaty of Nice and the new rules proposed by the Council of the European Union.

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  • Alonso-Meijide, J.M. & Bilbao, J.M. & Casas-Méndez, B. & Fernández, J.R., 2009. "Weighted multiple majority games with unions: Generating functions and applications to the European Union," European Journal of Operational Research, Elsevier, vol. 198(2), pages 530-544, October.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:2:p:530-544
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    2. Pongou, Roland & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Power theories for multi-choice organizations and political rules: Rank-order equivalence," Operations Research Perspectives, Elsevier, vol. 1(1), pages 42-49.
    3. D'ora Gr'eta Petr'oczy & L'aszl'o Csat'o, 2023. "Voting power in the Council of the European Union: A comprehensive sensitivity analysis," Papers 2312.16878, arXiv.org.
    4. Antônio Francisco Neto & Carolina Rodrigues Fonseca, 2019. "An approach via generating functions to compute power indices of multiple weighted voting games with incompatible players," Annals of Operations Research, Springer, vol. 279(1), pages 221-249, August.
    5. Freixas, Josep & Tchantcho, Bertrand & Tedjeugang, Narcisse, 2014. "Achievable hierarchies in voting games with abstention," European Journal of Operational Research, Elsevier, vol. 236(1), pages 254-260.
    6. Freixas, Josep & Kurz, Sascha, 2013. "The golden number and Fibonacci sequences in the design of voting structures," European Journal of Operational Research, Elsevier, vol. 226(2), pages 246-257.
    7. Stefano Benati & Giuseppe Vittucci Marzetti, 2021. "Voting power on a graph connected political space with an application to decision-making in the Council of the European Union," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 733-761, November.
    8. Smart, Richard D. & Blum, Matthias & Wesseler, Justus, 2015. "EU Member States’ Voting for Authorizing Genetically Engineered Crops: a Regulatory Gridlock," German Journal of Agricultural Economics, Humboldt-Universitaet zu Berlin, Department for Agricultural Economics, vol. 64(04), December.
    9. Antônio Francisco Neto, 2019. "Generating Functions of Weighted Voting Games, MacMahon’s Partition Analysis, and Clifford Algebras," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 74-101, February.
    10. Bolus, Stefan, 2011. "Power indices of simple games and vector-weighted majority games by means of binary decision diagrams," European Journal of Operational Research, Elsevier, vol. 210(2), pages 258-272, April.
    11. Freixas, Josep & Marciniak, Dorota & Pons, Montserrat, 2012. "On the ordinal equivalence of the Johnston, Banzhaf and Shapley power indices," European Journal of Operational Research, Elsevier, vol. 216(2), pages 367-375.
    12. A. Saavedra-Nieves & M. G. Fiestras-Janeiro, 2021. "Sampling methods to estimate the Banzhaf–Owen value," Annals of Operations Research, Springer, vol. 301(1), pages 199-223, June.
    13. A. Saavedra-Nieves, 2023. "On stratified sampling for estimating coalitional values," Annals of Operations Research, Springer, vol. 320(1), pages 325-353, January.
    14. Bhattacherjee, Sanjay & Chakravarty, Satya R. & Sarkar, Palash, 2022. "A General Model for Multi-Parameter Weighted Voting Games," MPRA Paper 115407, University Library of Munich, Germany.
    15. Wilms, Ingo, 2020. "Dynamic programming algorithms for computing power indices in weighted multi-tier games," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 175-192.
    16. Josep Freixas & Roberto Lucchetti, 2016. "Power in voting rules with abstention: an axiomatization of a two components power index," Annals of Operations Research, Springer, vol. 244(2), pages 455-474, September.

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