   # Create a voting system with three members that is a dictatorship. Calculate the Banzhaf power index for each voter 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 5EE
Textbook Problem
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## Create a voting system with three members that is a dictatorship. Calculate the Banzhaf power index for each voter for this system using the alternative definition.

To determine

Create a voting system with three members that is a dictatorship Calculate the Banzhaf power index for each voter for this system using the alternative definition.

### Explanation of Solution

Given Information:

Banzhaf Power indices

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, and C and the weighted system is {18:18,7,3}.

 Winning Coalition Number of Votes Critical Votes {A,B} 25 {A} {A,C} 21 {A} {A,B,C} 28 {A}

Blocking Coalition table is

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