   # Calculate, if possible, the l3anzhaf power index for each voter. Round to the nearest hundredth. { 14 : 6 , 6 , 4 , 3 , 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 10ES
Textbook Problem
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## Calculate, if possible, the l3anzhaf power index for each voter. Round to the nearest hundredth. { 14 : 6 , 6 , 4 , 3 , 1 }

To determine

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

{14:6,6,4,3,1}

### Explanation of Solution

Given Information:

The weighted system is {14:6,6,4,3,1}

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 {14:6,6,4,3,1}

Therefore,

 Winning coalition Number of Votes Critical voters {A,B,C} 16 {A,B,C} {A,B,D} 15 {A,B,D} {A,B,C,D} 19 {A,B} {A,B,C,E} 17 {A,B,C} {B,C,D,E} 14 {B,C,D,E} {A,B,C,D,E} 20 None

In above table we look in Critical voters' column and find that A is a critical voter 4 times, B is a critical voter is 5 times, C is a critical voter is 3 times, and D is a critical voter 2 times and E is a critical voter 1 times, therefore

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