Explanation Approach: Banzhaf power index is used to measure the voting power. A voters Banzhaf power index in a weighted voting system is given as = n u m b e r o f t i m e s t h e v o t e r i s c r i t i t c a l i n w i n n i n g c o a l i t i o n s t h e t o t a l n u m b e r o f t i m e s v o t e r s a r e c r i t i c a l i n w i n n i n g c o a l i t i o n s . Ex: 12 : 1 , 7 , 10 The number of voters = 3 Set of possible coalitions = 2 3 - 1 = 8 - 1 = 7 Here the quota is 12 . List out all possible coalitions one by one. Coalitions Weight Winning ( ≥ quota) { 1 } 1 No { 7 } 7 No { 10 } 10 No { 1 , 7 } 8 No 1 , 10 11 No { 7 , 10 } 17 Yes 1 , 7 , 10 18 Yes Therefore, there are two winning coalition i.e. { 7 , 10 } and { 1 , 7 , 10 } as the weights are greater than or equal to 12 (quota). In this winning coalitions, if any of the voters leave the coalition, then the coalition will be no longer winning. Such necessary voters are called critical voters. In 7 , 10 , if 7 left, then the weight of coalition = 17 - 7 = 10 . It is less than the quota. It will be then no longer a winning coalition. So, it is a critical voter. If 10 left, then the weight of coalition = 17 - 10 = 7 . It is less than the quota. It will be then no longer a winning coalition. So, it is a critical voter. Both are critical voters for { 7 , 10 } . Next winning coalition is 1 , 7 , 10 If 1 left, then the weight of coalition = 18 - 1 = 17 . It is more than the quota. So, it is not a critical voter. If 7 left, then the weight of coalition = 18 - 7 = 11 . It is less than the quota. It will be then no longer a winning coalition. So, it is a critical voter. If 10 left, then the weight of coalition = 18 - 10 = 8 . It is less than the quota. It will be then no longer a winning coalition. So, it is a critical voter. Critical voters for { 1 , 7 , 10 } are 7 , 10 Critical voters for the given weighted voting system are Coalitions Weight Critical voters { 7 , 10 } 17 7 , 10 1 , 7 , 10 18

6th Edition

ISBN: 9780134462356

Author: Pirnot

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 11.3, Problem 41E

To determine

To calculate:

The Banzhaf power index for each state, the quota in the weighted system is 21.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.3, Problem 40E

Chapter 11.3, Problem 42E

Students have asked these similar questions

Fill in the blanks to write the calculus problem that would result in the following integral (do not evaluate the interval). Draw a graph representing the problem. π/2 So/² 2xcosx dx Find the volume of the solid obtained when the region under the curve 38,189 on the interval is rotated about the axis.

Let f(x) = -5x-1, g(x) = x² + 5, h(x) = · x+4 3 Find (hog of)(1). (hogof)(1)= (Simplify your answer. Type an integer or a decimal.)

For the given function, find (a) the equation of the secant line through the points where x has the given values and (b) the equation of the tangent line when x has the first value. y= f(x) = x²+x; x=-1,x=2 a. Which of the following formulas can be used to find the slope of the secant line? ○ A. 2-(-1) f(2) f(-1) 2+(-1) C. 1(2)+(-1) The equation of the secant line is 1(2)+(-1) О в. 2+(-1) f(2)-(-1) D. 2-(-1)

Chapter 11 Solutions

Mathematics All Around-Workbook

Ch. 11.1 - Four candidates running for a vacant seat on the...Ch. 11.1 - Five candidates running for mayor receive votes as...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The drama society members are voting for the type...Ch. 11.1 - The drama society members are voting for the type...Ch. 11.1 - The drama society members are voting for the type...Ch. 11.1 - The drama society members are voting for the type...

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 index for each state, the quota in the weighted system is 21 .

Solution Summary: The author explains how the Banzhaf power index is used to measure the voting power in a weighted voting system.

Videos

To calculate:

The Banzhaf power index for each state, the quota in the weighted system is 21.

Want to see the full answer?

Chapter 11 Solutions

The Banzhaf power index for each state, the quota in the weighted system is 21 .

Solution Summary: The author explains how the Banzhaf power index is used to measure the voting power in a weighted voting system.

Videos

To calculate: The Banzhaf power index for each state, the quota in the weighted system is 21.

Want to see the full answer?

Chapter 11 Solutions

To calculate:

The Banzhaf power index for each state, the quota in the weighted system is 21.