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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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    File URL: http://arxiv.org/pdf/1812.07048
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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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