英文标题：
《Double Majority and Generalized Brexit: Explaining Counterintuitive
  Results》
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作者：
Werner Kirsch, Wojciech S{\\l}omczy\\\'nski, Dariusz Stolicki, Karol
  \\.Zyczkowski
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最新提交年份：
2018
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英文摘要：
  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.
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中文摘要：
本文对根据《里斯本条约》运作的欧盟理事会投票权分配进行了数学分析。我们研究了脱欧对剩余成员国投票权的影响，用彭罗斯-班扎夫指数衡量。我们注意到，所讨论的影响在投票权重方面是非单调的，一些成员国将在脱欧后失去权力。我们在双多数博弈中使用Penrose-Banzhaf指数的正态近似，以表明这种非单调性在大多数情况下是双多数系统固有的，但由于欧盟人口向量的特殊性而大大加剧。此外，我们还调查了假设的“普遍脱欧”的后果，即另一个成员国（来自28个成员国的联盟）的NN退出，注意到在大多数情况下，对投票权的影响是非单调的，但强烈取决于离开联盟的国家的大小。
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分类信息：

一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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