   # Calculate, if possible, the l3anzhaf power index for each voter. Round to the nearest hundredth. { 85 : 55 , 40 , 25 , 5 } ### 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 12ES
Textbook Problem
1 views

## Calculate, if possible, the l3anzhaf power index for each voter. Round to the nearest hundredth. { 85 : 55 , 40 , 25 , 5 }

To determine

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

{85:55,40,25,5}

### Explanation of Solution

Given Information:

The weighted system is {85:55,40,25,5}

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 and D, and the weighted system is {85:55,40,25,5}.

Therefore,

 Winning Coalition Number of Votes Critical Voters {A,B} 95 {A,B} {A,B,C} 120 {A,B} {A,B,D} 100 {A,B} {A,C,D} 85 {A,C,D} {A,B,C,D} 125 {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 times, and D is a critical voter 1 time, therefore

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