   # Calculate, if possible, the l3anzhaf power index for each voter. Round to the nearest hundredth. { 18 : 18 , 7 , 3 , 3 , 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 9ES
Textbook Problem
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## Calculate, if possible, the l3anzhaf power index for each voter. Round to the nearest hundredth. { 18 : 18 , 7 , 3 , 3 , 1 , 1 }

To determine

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

{18:18,7,3,3,1,1}.

### Explanation of Solution

Given Information:

The weighted system {18:18,7,3,3,1,1}

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,E and F and the weighted system is {18:18,7,3,3,1,1}.

Therefore,

 Winning Coalition Number of Votes Critical Voters {A,B} 25 {A} {A,C} 21 {A} {A,D} 21 {A} {A,E} 19 {A} {A,F} 19 {A} {A,B,C} 28 {A} {A,B,D} 28 {A} {A,B,E} 26 {A} {A,B,F} 26 {A} {A,B,C,D} 31

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