Abstract
This article anlayses the change in the balance of power in the European Union Council due to the United Kingdom leaving (referred to as Brexit). This analysis is based on the concept of power indices in voting games where natural coalitions, called pre-coalitions, occur between various players (or parties). The pre-coalitions in these games are assumed to be formed around the six largest member states (after Brexit, the five largest), where each of the remaining member states joins the pre-coalition based around the large member state which is the most similar according to the subject of the vote. This is illustrated by an example. We consider adaptations of three classical indices: the Shapley-Shubik, Banzhaf-Penrose and Johnston indices based on the concept of a consistent share function (also called quotient index). This approach can be interpreted as a two-level process of distributing power. At the upper level, power is distributed amongst pre-coalitions. At the lower level, power is distributed amongst the members of each pre-coalition. One of the conclusions of the research is that removing the UK from the voting game means that the power indices of small countries actually decrease. This seems somewhat surprising as the voting procedure in the EU council was designed to be robust to changes in the number and size of member states. This conclusion does not correspond to a general result, but does indicate the difficulty of defining voting rules which are robust to changes in the set of players.
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Mercik, J., Ramsey, D.M. (2017). The Effect of Brexit on the Balance of Power in the European Union Council: An Approach Based on Pre-coalitions. In: Mercik, J. (eds) Transactions on Computational Collective Intelligence XXVII. Lecture Notes in Computer Science(), vol 10480. Springer, Cham. https://doi.org/10.1007/978-3-319-70647-4_7
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DOI: https://doi.org/10.1007/978-3-319-70647-4_7
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