Math for Liberal Studies: Banzhaf Power Index

[HamblinMath]

It turns out (but it's not at all obvious) that the number of times a voter is critical in winning coalitions is equal to the number of times he/she is critical in blocking coalitions.

[afterapplepicking]

My book doesn't say anything about blocking coalitions. It says the way to find the Benzahf power index is to find every possible winning coalition. Count up the number of times a single player is critical in those winning coalitions (X), and and then count up how many times ANY player is critical in a winning coalition (Y). X/Y = the answer. Not a word about blocking coalitions.

Is that wrong, or will it lead to the same answer as what you're getting with your method?

[Ohemgee35]

Thanks so much! Was really helpful info.