Calculate the Shapley-Shubik power index for each voter in the weighted voting system [6: 5, 3, 1].
A) (1, 0, 0)
B) (2/3, 1/6, 1/6)
C) (1/3, 1/3, 1/3)
D) (1/2, 1/2, 0)

Question

Quizplus · Accepted Answer

The Shapley-Shubik power index calculates the average marginal contributions of each voter to every possible winning coalition. In this case, the total number of possible winning coalitions is 2^3 - 1 = 7.

To calculate the power index for each voter, we need to first calculate their marginal contributions to each coalition. For example, if voter 1 joins a coalition that already has 6 votes, their marginal contribution is 6 - 5 = 1. Once we have calculated the marginal contributions for all voters in all winning coalitions, we can add up the contributions for each voter and divide by the total number of coalitions.

Using this method, we find that the power indices for each voter are:
Voter 1: 2/3
Voter 2: 1/6
Voter 3: 1/6

Therefore, the best choice is B, as it correctly identifies the power indices for each voter.

Calculate the Shapley-Shubik Power Index for Each Voter in the Weighted