Paper presented at the Workshop on Voting and Collective Decision Making

Analysis of the Constitutional Treaty of the European Union shows that there is a serious discrepancy between the power of Member States as computed by the two main power indices, namely those of Shapley-Shubik and Banzhaf, and also in terms of the power gradient, a non-parametric measure of the overall distribution of power. Given the lack of compelling arguments to choose between these indices on purely axiomatic grounds, we turn to a probabilistic approach as pioneered by Straffin (1977). A new definition of power indices as expected decisiveness shows that the defining feature of each approach is a particular distribution of the voting poll. Empirical evidence drawn from yes-no voting situations, in addition a consideration of first principles, leads us to reject one of these approaches. Useful related concepts of efficiency and blocking leverage, previously used solely by a ‘Banzhaf’ approach are developed for the case of Shapley-Shubik and a comparison of results is shown