   # Consider the weighted voting system { 60 : 4 , 56 , 58 } . a. Compute the Banzhaf power index for each voter in this system. b. Voter B has a weight of 56 compared with 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. ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4.3, Problem 25ES
Textbook Problem
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## Consider the weighted voting system { 60 : 4 , 56 , 58 } .a. Compute the Banzhaf power index for each voter in this system.b. Voter B has a weight of 56 compared with 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.

To determine

(a)

Compute the Banzhaf power index Vor each voter in this system.

### Explanation of Solution

Given Information:

Three people A,B andC, and weighted system is {60:4,56,58}.

Concept used:

BPI(v)=Number of times voter v is a critical voterNuner of times any voter is a critical voter

Calculation:

Consider three people A,B andC, and weighted system is {60:4,56,58}.

Therefore,

 Winning Coalition Number of Votes Critical Voters {A,B} 6 {A,B} {A,C} 62 {A,C} {B,C} 114 {B,C} {A,B
To determine

(b)

Voter B has a weight of 56 compared with 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.

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