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 } To determine b) To explain: How does this conform with your intuition.

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ISBN: 9780134462356

Author: Pirnot

Publisher: PEARSON

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Chapter 11.3, Problem 36E

To determine

a)

The Banzhaf power index for each voter in the weighted voting system 12:1,1,1,1,1,1,1,1,1,1,1,1.

To determine

b)

To explain:

How does this conform with your intuition.

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Chapter 11.3, Problem 35E

Chapter 11.3, Problem 37E

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a) The Banzhaf power index for each voter in the weighted voting system 12 : 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 .

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

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a)

The Banzhaf power index for each voter in the weighted voting system 12:1,1,1,1,1,1,1,1,1,1,1,1.

b)

To explain:

How does this conform with your intuition.

Want to see the full answer?

Chapter 11 Solutions

a) The Banzhaf power index for each voter in the weighted voting system 12 : 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 .

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

Concept explainers

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a) The Banzhaf power index for each voter in the weighted voting system 12:1,1,1,1,1,1,1,1,1,1,1,1.

b) To explain: How does this conform with your intuition.

Want to see the full answer?

Chapter 11 Solutions

a)

The Banzhaf power index for each voter in the weighted voting system 12:1,1,1,1,1,1,1,1,1,1,1,1.

b)

To explain:

How does this conform with your intuition.