Voting Power in the Council of the European Union under the Nice rules

We provide a new method to compute the Banzhaf power index for weighted voting games as well as weighted double and triple majority games. We calculate the Banzhaf index in an exact way by generating functions, with a signi...cant decrease in the computational complexity. Moreover, the Banzhaf indices are calculated for the decision rules approved in the Nice summit meeting, which will be used in the European Union enlarged to 27 countries. We show that the triple majority rules adopted are quasi equivalent to weighted voting or double majority games, since the required population quota to approve a decision does not change the voting power of the countries. Finally, we conclude with some contradictions found in the Treaty of Nice.