The Council of the European Union (EU) is one of the main decision-making bodies of the EU. Many 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 influence of the two countries with about 4% of the total population each is found to be almost flat. The level of decisiveness decreases if the population criterion is above 68% or the states criterion is at least 17. 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 to evaluate any proposal for reforming the qualified majority voting system.

翻译：欧洲联盟理事会（欧盟）是欧盟的主要决策机构之一。许多决策需要特定多数支持：55%的成员国（目前为15个）的支持，且这些国家需代表至少65%的总人口。我们研究了在合理范围内修改这些标准时，基于Shapley-Shubik指数的权力分配及获胜联盟比例的变化。发现两个各占总人口约4%的国家的权力影响几乎持平。若人口标准高于68%或成员国标准至少为17，决策确定性水平将下降。获胜联盟的比例可从13.2%增加至20.8%（30.1%），同时Shapley-Shubik指数的最大相对变化保持在3.5%（5.5%）以下。我们的结果对于评估任何改革特定多数投票制度的提案至关重要。