The weighted voting systems for the voters A, B, C, ... are given in the form

{q: w₁, w₂, w₃, w₄, ..., w_n}.

The weight of voter A is w₁, the weight of voter B is w₂, the weight of voter C is w₃, and so on. Consider the weighted voting system {65: 4, 61, 62}. (a) Compute the Banzhaf power index for each voter in this system. (Round your answers to the nearest hundredth.)

BPI(A)	=
BPI(B)	=
BPI(C)	=

(b) Voter B has a weight of 61 compared to only 4 for voter A, yet the results of part (a) show that voter A and voter B both have the same Banzhaf power index. Explain why it seems reasonable, in this voting system, to assign voters A and B the same Banzhaf power index. Despite the varied weights, this is a majority system. Any two of the three voters are needed for a quota

A. Despite the varied weights, this is a dictator system. Voter C controls the outcome, while voters A and B are dummy voters.

B. Despite the varied weights, in this system, all of the voters are needed for a quota.

C. Despite the varied weights, in this system, all voters are dummy voters. No voter is critical to a successful outcome.

D. Despite the varied weights, this is a minority system. Any one of the three voters can stop a quota.