The Shapley–Shubik power index in a voting situation depends on the number of orderings
in which each player is pivotal. The Banzhaf power index depends on the number of ways in
which each voter can effect a swing. If the input size of the problem is n, then the function
which measures the worst case running time for computing these indices is in O n2 n. We
present a method based on generating functions to compute these power indices efficiently
for weighted multiple majority games and we study the temporal complexity of the …