   # Calculate the Banzhaf power indices for voters A, B, C, D, and E in the one-person, one-vote system { 3 : 1 , 1 , 1 , 1 , 1 } . ### 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, Problem 24RE
Textbook Problem
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## Calculate the Banzhaf power indices for voters A, B, C, D, and E in the one-person, one-vote system { 3 : 1 , 1 , 1 , 1 , 1 } .

To determine

Calculate the Banzhaf power indices for voters A,B,C,D and E in the one person, one vote system {3:1,1,1,1,1}.

### Explanation of Solution

Given Information:

Consider four people A,B,C,D and E and the weighted system is {3:1,1,1,1,1}.

Concept used:

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

Calculation:

Consider four people A,B,C,D and E and the weighted system is {3:1,1,1,1,1}.

Therefore,

 Winning Coalition Number of Votes Critical voters {A,B,C} 3 {A,B,C} {A,B,D} 3 {A,B,D} {A,B,E} 3 {A,B,E} {A,C,D} 3 {A,C,D} {A,C,E} 3 {A,C,E} {A,D,E} 3 {A,D,E} {B,C,D} 3 {B,C,D} {B,C,E} 3 {B,C,E} {B,D,E} 3 {B,D,E} {

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