Given the weighted voting system [6: 4, 3, 2, 1], calculate the Banzhaf power index.
A) (11, 6, 2, 2)
B) (5, 4, 4, 1)
C) (10, 6, 2, 2)
D) (10, 6, 6, 2)

Question

Quizplus · Accepted Answer

To calculate the Banzhaf power index, we count the number of swing voters for each member of the coalition (i.e. the number of times they hold the pivotal vote which changes the outcome of the vote).

Starting with member A (who has a weight of 6), we can see that they have the ability to determine the outcome of the vote if they receive the support of either member B or member C. Therefore, A has 2 swing voters.

For member B (who has a weight of 4), they have the ability to determine the outcome of the vote if they receive the support of both members C and D. This means that B has 2 swing voters.

For member C (who has a weight of 3), they have the ability to determine the outcome of the vote if they receive the support of both members A and B. This means that C has 2 swing voters.

Finally, for member D (who has a weight of 2), they only have the ability to determine the outcome of the vote if they receive the support of member A with either B or C being absent. This means that D has 2 swing voters.

Therefore, the Banzhaf power index for each member is (10, 6, 6, 2). The best choice is D, as it has the lowest Banzhaf power index and thus has the least influence in the coalition.

Given the Weighted Voting System [6: 4, 3, 2, 1]