This paper deals with the problem of calculating the Shapley-Shubik power index in weighted majority games. We propose an efficient Monte Carlo algorithm based on an implicit hierarchical structure of permutations of players. Our algorithm outputs a vector of power indices preserving the...

While they use the language of game theory known measures of a priory voting power are hardly more than statistical expectations assuming voters behave randomly. Focusing on normalised indices we show that rational players would behave differently from the indices predictions and propose a model...

The concept of fair representation of voters in a committee representing different voters' groups, such as national representations in union of states, is discussed. This concept, introduced into discussion about voting rights in the Council of European Union in 2004, was narrowed to proposal of...

The European Union (EU) is not de jure a federation, but after 50 years of institutional evolution it possesses attributes of a federal state. One can conclude that EU is something betweenʺ federation and intergovernmental organization. If we measure something betweenʺ by interval [0, 1],...