   # Calculate, if possible, the l3anzhaf power index for each voter. Round to the nearest hundredth. { 3 : 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 4.3, Problem 8ES
Textbook Problem
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## Calculate, if possible, the l3anzhaf power index for each voter. Round to the nearest hundredth. { 3 : 1 , 1 , 1 , 1 }

To determine

Calculate, if possible, the Banzhaf power index for each voter. Round to the nearest hundredth.

{3:1,1,1,1}

### Explanation of Solution

Given Information:

The weighted system is {3:1,1,1,1}

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,C,D} 3 {A,C,D} {B,C,D} 3 {B,C,D} {A,B,C,D} 4 None

In above table we look in Critical voters' column and find that A is a critical voter 3 times, B is a critical voter is 3 times, C is a critical voter is 3 times, and D is a critical voter 3 times therefore

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