Double Majority and Generalized Brexit: Explaining Counterintuitive Results
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.
Cite
@article{arxiv.1812.07048,
title = {Double Majority and Generalized Brexit: Explaining Counterintuitive Results},
author = {Werner Kirsch and Wojciech Słomczyński and Dariusz Stolicki and Karol Życzkowski},
journal= {arXiv preprint arXiv:1812.07048},
year = {2019}
}
Comments
32 pages, 10 pages, 10 figures