is a voters weight the same as the voters Banzhaf index in a

Solution

No, a voter\'s weight is not the same as the voter\'s Banzhaf index.

Consider an example where the voter\'s weights are

[4, 3, 2, 1] for A, B, C, D respectively

And the measure requires let say 6 votes to pass.

Here the number of swing votes for A will be in the cases of the following voted groups

B, C, BC, BD, CD

The decision of A\'s vote along with the above given cases decides the outcome of the result.

So, A.s Banzhaf index is 5/12.

Similarly Banzhaf index for B = 3/12, c= 3/12 and D = 1/12

Note here that the index is normalized.

From this you can see that the weights are not the same as the Banzhaf indexes.