Double Majority and Generalized Brexit: Explaining Counterintuitive Results

TL;DR

This paper analyzes how Brexit and hypothetical exits affect voting power in the EU Council, revealing non-monotonic effects due to the double-majority system and population distribution.

Contribution

It provides a mathematical analysis of voting power changes in the EU Council under Brexit and generalized exits, highlighting inherent non-monotonic effects.

Findings

Brexit can cause some member states to lose voting power.

Non-monotonic effects are inherent in the double-majority system.

Effects depend strongly on the size of the exiting member state.

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.