Explanation Given: In Cleansburg the city council has four members and a strong mayor who has a vote as well as the power to veto motions supported by a simple majority of the council members but the mayor cannot veto motions supported by all four council members. Thus a motion can pass if the mayor and two or more council members support it or if mayor is against it but four council members support it. Approach: In a winning coalition, a player without whom the coalition would be a losing coalition then they player is critical player. The critical count for each player is the number of winning coalition in which the player is a critical player. The Banzhaf power index for each player is the ratio of player’s critical count and the total critical count of all players. If B is the player’s critical count and T is the total critical count of all the players then the Banzhaf power index is, β = B T × 100 . Calculation: Let the weight of the mayor be m and council members be c . The quota is represented by q . The voting system is represented by [ q : m , c , c , c , c ] . From the given information, the quota should satisfy the following equalities, q = m + 2 c … ( 1 ) q = 4 c … ( 2 ) Equating equation ( 1 ) and equation ( 2 ) . m + 2 c = 4 c m = 2 c The value of council members vote is 1. So, m = 2 and q = 4 . The voting system is [ 4 : 2 , 1 , 1 , 1 , 1 ] The different sequential coalitions for [ 4 : 2 , 1 , 1 , 1 , 1 ] with pivotal player (Pivot Players are underlined) is, 〈 M _ , P 1 _ , P 2 _ 〉 〈 M _ , P 2 _ , P 4 _ 〉 〈 M _ , P 1 _ , P 3 _ 〉 〈 M _ , P 3 _ , P 4 _ 〉 〈 M _ , P 1 _ , P 4 _ 〉 〈 P 1 _ , P 2 _ , P 3 _ , P 4 _ 〉 〈 M _ , P 2 _ , P 3 _ 〉 〈 M , P 1 , P 2 , P 3 , P 4 〉 For the mayor the critical count is 6 and for the council members the critical count is 4

Excursions in Mathematics, Loose-Leaf Edition Plus MyLab Math with Pearson eText -- 18 Week Access Card Package

9th Edition

ISBN: 9780136208754

Author: Tannenbaum, Peter

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 2, Problem 76E

To determine

To find:

The Banzhaf power distribution.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2, Problem 75E

Chapter 2, Problem 77E

Students have asked these similar questions

3. Use the method of washers to find the volume of the solid that is obtained when the region between the graphs f(x) = √√2 and g(x) = secx over the interval ≤x≤ is rotated about the x-axis.

4. Use cylindrical shells to find the volume of the solid generated when the region enclosed by the given curves is revolved about the x-axis. y = √√x, y = 0, y = √√3

5 4 3 21 N -5-4-3-2 -1 -2 -3 -4 1 2 3 4 5 -5+ Write an equation for the function graphed above y =

Chapter 2 Solutions

Excursions in Mathematics, Loose-Leaf Edition Plus MyLab Math with Pearson eText -- 18 Week Access Card Package

Ch. 2 - Five partners (P1,P2,P3,P4, andP5) jointly own the...Ch. 2 - Five partners (P1,P2,P3,P4, andP5) jointly own the...Ch. 2 - Prob. 3E Ch. 2 - Prob. 4E Ch. 2 - In each of the following weighted voting systems,...Ch. 2 - In each of the following weighted voting systems,...Ch. 2 - Consider the weighted voting system[q:7,5,3]. Find...Ch. 2 - Consider the weighted voting system...Ch. 2 - A committee has four members (P1,P2,P3,andP4). In...Ch. 2 - A committee has six members...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The Banzhaf power distribution.

Solution Summary: The author explains the Banzhaf power distribution, which is given by beta and the voting system.

Videos

To find: The Banzhaf power distribution.

Want to see the full answer?

Chapter 2 Solutions

To find:

The Banzhaf power distribution.