Abstract
AbstractThe problem of designing an optimal weighted voting system for the two-tier voting, applicable in the case of the Council of Ministers of the European Union (EU), is investigated. Various arguments in favor of the square root voting system, in which voting weights of member states are proportional to the square root of their population. It is known that the voting power of every member state is approximately equal to its voting weight, if the threshold \(q\) for the qualified majority in the voting body is optimally chosen. We analyze the square root voting system for a generic ‘union’ of \(M\) states and derive in this case an explicit approximate formula for the level of the optimal threshold: \(q\simeq 1/2+1/\sqrt{\pi M}\).KeywordsEuropean UnionMember StateVote SystemSmall StateLarge StateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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