Voting Power in the Council of the European Union: A Comprehensive Sensitivity Analysis

Abstract The Council of the European Union (EU) is one of the main decision-making bodies of the EU. A number of decisions require a qualified majority, the support of 55% of the member states (currently 15) that represent at least 65% of the total population. We investigate how the power distribution based on the Shapley–Shubik index and the proportion of winning coalitions change if these criteria are modified within reasonable bounds. The power of the two countries, with approximately 4% of the total population each, is found to be almost flat. The decisiveness index decreases if the population criterion is above 68% or the states criterion is at least 17. Some quota combinations contradict the principles of double majority. The proportion of winning coalitions can be increased from 13.2% to 20.8% (30.1%) such that the maximal relative change in the Shapley–Shubik indices remains below 3.5% (5.5%). Our results are indispensable for evaluating any proposal to reform the qualified majority voting system.