Question

The weighted voting systems for the voters A, B, C, ... are given in the form q: w1, w2, w3, w4, ..., wn . The weight of voter A is w1, the weight of voter B is w2, the weight of voter C is w3, and so on.

Calculate, if possible, the Banzhaf power index for each voter. Round to the nearest hundredth. (If not possible, enter IMPOSSIBLE.)

{10: 7, 6, 4}

BPI(A) =

BPI(B) =

BPI(C) =

Answer 1

Banzhaf power index is calculated as follows

-> First we will list all winning coalitions

-> In each coalition, we will identify those players who are critical

-> Then we will count how many times each player is critical

-> At last we will convert these counts to fractions or decimals by dividing by the total times any player is critical