Preferences, the agenda setter, and the distribution of power in the EU

In this paper, we present a generalization of power indices which includes the preferences of the voters. Using a Multilinear Extension perspective (Owen in Manage Sci 18:p64-p72, 1972a) we measure the probability of the players' voting "yes" for a particular political issue. Further, we randomize the issues and show the influence that the Agenda Setter can have on a player's power. We demonstrate these results using data from the European Union to show how the power distribution may shift after enlargement and under the new Constitutional Treaty.