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. Consider the weighted voting system {73: 4, 69, 71}. (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 69 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: a) Despite the varied weights, in this system, all of the voters are needed for a quota. b) Despite the varied weights, this is a dictator system. Voter C controls the outcome, while voters A and B are dummy voters. 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. e) Despite the varied weights, this is a majority system. Any two of the three voters are needed for a quota
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. Consider the weighted voting system {73: 4, 69, 71}. (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 69 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: a) Despite the varied weights, in this system, all of the voters are needed for a quota. b) Despite the varied weights, this is a dictator system. Voter C controls the outcome, while voters A and B are dummy voters. 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. e) Despite the varied weights, this is a majority system. Any two of the three voters are needed for a quota
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section: Chapter Questions
Problem 8T
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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.
Consider the weighted voting system {73: 4, 69, 71}.
(a) Compute the Banzhaf power index for each voter in this system. (Round your answers to the nearest hundredth.)
(b) Voter B has a weight of 69 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:
BPI(A) | = | |
BPI(B) | = | |
BPI(C) | = |
(b) Voter B has a weight of 69 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:
a) Despite the varied weights, in this system, all of the voters are needed for a quota.
b) Despite the varied weights, this is a dictator system. Voter C controls the outcome, while voters A and B are dummy voters.
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.
e) Despite the varied weights, this is a majority system. Any two of the three voters are needed for a quota.
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