Empirical Banzhaf indices

This paper considers a generalization of the Banzhaf index which is used to quantify voting power in constituent bodies. The generalization allows unequal probabilities in voting outcomes and relies on historical voting data to highlight natural coalitions that exist between various constituent bodies. The approach is based on Bayesian modelling where estimates of voting probabilities are given by the posterior means of Dirichlet distributions. An example is provided concerning the voting power of provinces according to the amending formula to Canada's Constitution.