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The Council of the European Union (EU) is one of the main decision-makingbodies of the EU. Many decisions require a qualified majority: the support of55% of the member states (currently 15) that represent at least 65% of thetotal population. We investigate how the power distribution, based on theShapley-Shubik index, and the proportion of winning coalitions change if thesecriteria are modified within reasonable bounds. The influence of the twocountries with about 4% of the total population each is found to be almostflat. The level of decisiveness decreases if the population criterion is above68% or the states criterion is at least 17. The proportion of winningcoalitions can be increased from 13.2% to 20.8% (30.1%) such that the maximalrelative change in the Shapley--Shubik indices remains below 3.5% (5.5%). Ourresults are indispensable to evaluate any proposal for reforming the qualifiedmajority voting system.

Voting power in the Council of the European Union: A comprehensive sensitivity analysis