Exam 11: Weighted Voting Systems

Evaluate ₈C₇.

In the weighted voting system [8: 5, 2, 2, 2, 2, 2], find the Banzhaf power index for voter B.

In a weighted voting system, the Banzhaf power index of each voter is directly proportional to the weight of the vote.

In a weighted voting system, the Banzhaf power index of a dummy voter is 0.

In a weighted voting system with eight voters, how many coalitions would there be in which exactly five members voted YES?

A weighted voting system has 12 members. How many distinct coalitions are there in which exactly seven members vote YES?

Use the weighted voting system [12: 4, 4, 3, 3, 2, 1] to answer the following questions -Is any voter a dummy voter?

Calculate the Shapley-Shubik power index for each voter in the system [8: 5, 4, 3].

Use the weighted voting system [10: 7, 4, 3, 3, 1] to answer the following Questions -Which of the voters are dummy voters?

Given the weighted voting system [16: 3, 9, 4, 5, 10], calculate the Banzhaf power index for each voter.

In a weighted voting system, all winning coalitions would become blocking coalitions if each voter switched his or her vote from YES to NO.

A weighted voting system has 10 members. How many distinct coalitions are there in which exactly six members vote yes?

Given the weighted voting system [7: 4, 1, 1, 1, 1, 1], find the Banzhaf power index for each voter.

Calculate the Shapley-Shubik power index for the weighted voting system [8: 6, 1, 1, 1, 1, 1].

Use the weighted voting system [12: 4, 4, 3, 3, 2, 1] to answer the following questions -Give two blocking coalitions.

Given the weighted voting system [19: 9, 7, 5, 3, 1], which of the voters are dummy voters?

Given the weighted voting system [5: 3, 2, 1, 1, 1], find which voters of the coalition {A, C, D, E} are critical.

Given weighted voting system of seven voters, the Banzhaf power index for voter A is 5. Find the probability that the voter A is a critical voter.

Given the weighted voting system [30: 20, 17, 10, 5], list all winning coalitions.

Use the weighted voting system [12: 8, 4, 4, 3, 3] to answer the following questions -Calculate the Banzhaf power index for this voting system.