🤖 AI Summary
This study systematically assesses the sensitivity of the EU Council’s double-majority voting rule (55% of member states plus 65% of the EU population) to variations in its dual thresholds, quantifying impacts on national voting power (measured by the Shapley–Shubik index), coalition decisiveness, and the proportion of winning coalitions.
Method: Employing combinatorial enumeration and parametric sensitivity analysis, we comprehensively characterize the robustness of power distribution across feasible threshold ranges—first such analysis under realistic constraints.
Results: We find that small states’ voting power remains approximately invariant; decisional efficiency declines markedly when the population threshold exceeds 68% or the member-state threshold exceeds 17 countries; an optimal threshold combination increases the share of winning coalitions to 30.1% (+20.8 percentage points over baseline) while constraining national power shifts to within ±5.5%. The study identifies critical quota combinations violating the double-majority principle and pinpoints key inflection points, providing quantitative foundations for EU institutional reform.
📝 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 about 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 in evaluating any proposal for reforming the qualified majority voting system.