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Double Majority and Generalized Brexit: Explaining Counterintuitive Results

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  • Werner Kirsch
  • Wojciech S{l}omczy'nski
  • Dariusz Stolicki
  • Karol .Zyczkowski

Abstract

A mathematical analysis of the distribution of voting power in the Council of the European Union operating according to the Treaty of Lisbon is presented. We study the effects of Brexit on the voting power of the remaining members, measured by the Penrose--Banzhaf Index. We note that the effects in question are non-monotonic with respect to voting weights, and that some member states will lose power after Brexit. We use the normal approximation of the Penrose--Banzhaf Index in double-majority games to show that such non-monotonicity is in most cases inherent in the double-majority system, but is strongly exacerbated by the peculiarities of the EU population vector. Furthermore, we investigate consequences of a hypothetical "generalized Brexit", i.e., NN-exit of another member state (from a 28-member Union), noting that the effects on voting power are non-monotonic in most cases, but strongly depend on the size of the country leaving the Union.

Suggested Citation

  • Werner Kirsch & Wojciech S{l}omczy'nski & Dariusz Stolicki & Karol .Zyczkowski, 2018. "Double Majority and Generalized Brexit: Explaining Counterintuitive Results," Papers 1812.07048, arXiv.org.
    • Handle: RePEc:arx:papers:1812.07048
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    References listed on IDEAS

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    1. Marc Feix & Dominique Lepelley & Vincent Merlin & Jean-Louis Rouet, 2007. "On the voting power of an alliance and the subsequent power of its members," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(2), pages 181-207, February.
    2. Rahhal Lahrach & Jérôme Le Tensorer & Vincent Merlin, 2005. "Who benefits from the US withdrawal of the Kyoto Protocol? An application of the MMEA method to measure power," Post-Print halshs-00010171, HAL.
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    Cited by:

    1. Philip D. Grech, 2021. "Power in the Council of the EU: organizing theory, a new index, and Brexit," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 223-258, February.
    2. Dóra Gréta Petróczy & Mark Francis Rogers & László Á. Kóczy, 2022. "Exits from the European Union and Their Effect on Power Distribution in the Council," Games, MDPI, vol. 13(1), pages 1-25, February.
    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, revised Sep 2024.

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