Approximation of Banzhaf indices and its application to voting games

In this paper, we propose an improved version of the power index related to the Banzhaf power index for weighted voting systems. This index now takes into account the mutual persuasion power matrix(PPM) existing among the voters. This improved index is calculated for European Union voting by basing the PPM on immigration data among the EU countries. We also provide better approximation bounds for the Monte Carlo approximation method for computing power indices.
Comment: 15 pages, 3 tables