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 power 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：欧盟理事会（EU）是欧盟的主要决策机构之一。许多决策需要特定多数支持：即获得代表至少65%总人口的55%成员国（目前为15国）的赞成。本研究探讨了若在合理范围内调整这些标准，基于夏普利-舒比克指数的权力分配以及获胜联盟比例将如何变化。研究发现，两个各占约4%总人口国家的权力曲线近乎平缓。当人口标准超过68%或国家标准达到至少17国时，决策效能水平将下降。获胜联盟比例可从13.2%提升至20.8%（30.1%），同时确保夏普利-舒比克指数的最大相对变化保持在3.5%（5.5%）以下。我们的研究结果为评估特定多数投票制度改革提案提供了不可或缺的参考依据。