   # Four voters. A. B. C. and D. make decisions by using the weighted voting system { 5 : 4 , 2 , 1 , 1 } . In the event of a tie, a fifth voter, E, casts a vote to break the tie, For this voting scheme, determine the Banzhaf power index for each voter, including voter E. ### 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 29RE
Textbook Problem
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## Four voters. A. B. C. and D. make decisions by using the weighted voting system { 5 : 4 , 2 , 1 , 1 } . In the event of a tie, a fifth voter, E, casts a vote to break the tie, For this voting scheme, determine the Banzhaf power index for each voter, including voter E.

To determine

Determine the Banzhaf power index for each voter, including voter E.

### Explanation of Solution

Given Information:

Four voters, A,B,C and D make decisions by using the weighted voting system {5:4,2,1,1} in the event of a tie, a fifth voter, E, casts a vote to break the tie.

Concept used:

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

Calculation:

Consider four voters A,B,C and D make decisions by using voting scheme {5:4,2,1,1}

If there is a tie then E cast their votes

 Winning Coalition (Without   E) Critical Voters Winning Coalition (   EVoting) Critical Voters {A,B} A,B {A,B,E} A,B {A,C} A,C {C,E} C,E {A,D} A,D {D,E} D,E {A,B,C} A {A,B,D} A {A,C,D} A &e

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