  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.
