The European integration process can be regarded as an aspect of the overall process of globalization and at the same time as an attempt to reconcile the move towards standardization with the defence of national diversity. A central role in the effort to exploit the benefits of integration without hampering the national nterest is the collective decision-making process in the EU shared by the Council and the Parliament, where national representatives struggle for the conquest of the ”lion’s share” in the division of the surplus stemming from the compromise on common policies. The paper focuses on the rationale behind the various Indices of Voting Power (Penrose, Banzhaf, Shapley and Shubik, Holler) which are the formal tools meant to understanding the coalition formation and assessing the probability of reaching an agreement. In the EU Council, although ministers tend to reach a broad consensus and explicit voting is rare, decision may be taken by qualified majority voting where countries are assigned weights reflecting their size. This practice has often been objected on the grounds that the potential emergence of permanent coalitions would prevent countries from being adequately represented, and eventually a different rule was proposed. The pros and cons of the newly proposed system are analysed through the computation of the Indices of Voting Power for the EU Council and Parliament.