   # Create a voting system with five members that satisfies the one-person. one-vote rule. Calculate the Banzhaf power index for this system using the alternative definition. ### 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 7EE
Textbook Problem
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## Create a voting system with five members that satisfies the one-person. one-vote rule. Calculate the Banzhaf power index for this system using the alternative definition.

To determine

Create a voting system with five members that satisfies the one-person, one-vote wie. Calculate the Banzhaf power index for this system using the alternative definition.

### Explanation of Solution

Given Information:

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:

 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} {A,B,C,D} 4 None {A,B,C,E} 4 None {A,B,D,E} 4 None {A,C,D,E} 4 None {B,C,D,E} 4 None {A,B,C,D,E} 5 None

Blocking coalition table is

 Winning Coalition Number of Votes Number of remaining votes Critical Voters {A,B,C} 3 2 {A,B,C} {A,B,D} 3 2 {A,B,D} {A,B,E} 3 2 {A,B,E} {A,C,D} 3 2 &e

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