   # Calculate, if possible, the l3anzhaf power index for each voter. Round to the nearest hundredth. { 10 : 7 , 3 , 2 , 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 5ES
Textbook Problem
1 views

## Calculate, if possible, the l3anzhaf power index for each voter. Round to the nearest hundredth. { 10 : 7 , 3 , 2 , 1 }

To determine

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

{10: 7, 3. 2, 1}

### 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 four people A,B,CandD, and the weighted system is {10: 7, 3. 2, 1}.

 Winning Coalition Number of Votes Critical Votes {A,B} 10 {A,B} {A,B,C} 12 {A,B} {A,B,D} 11 {A,B} {A,C,D} 10 {A,C,D} {A,B,C,D} 13 {A}

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

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