What is the difference between Banzhaf Power Index and Shapley-Shubik? For Shapeley-Shubik, I understand that σ1, for example = # of times P1 is critical over # of total critical numbers and a number is critical when it makes the coalition become a winning coalition. In cases with 4 players, T (total critical players) is always 24. Isn't BPI the same thing? I'm having a hard time understanding the difference. For example, I get the same answer when I am asked for BPI and Shapely Shubik for the same coalition (don't think that's the right term) for say, [16: 12, 4, 3, 1]
