   # Drama Department The four staff members. A, B,C, and D. of a college drama department use (he weighted voting system { 8 : 5 , 4 , 3 , 2 } to make casting decisions for a play they are producing. In this voting system, voter A has a weight of 5, voter B has a weight of 4, voter C has a weight of 3, and voter D has a weight of 2. Compute the Banzhaf power index for each member of the department. Round each result to the nearest hundredth. ### 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, Problem 9T
Textbook Problem
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## Drama Department The four staff members. A, B,C, and D. of a college drama department use (he weighted voting system { 8 : 5 , 4 , 3 , 2 } to make casting decisions for a play they are producing. In this voting system, voter A has a weight of 5, voter B has a weight of 4, voter C has a weight of 3, and voter D has a weight of 2. Compute the Banzhaf power index for each member of the department. Round each result to the nearest hundredth.

To determine

Compute The Banzhaf power index for each member of the department Round each result to the nearest hundredth.

### Explanation of Solution

Given Information:

The four staff members A,B,C and D of a college drama department use the weighted voting system {8:5,4,3,2} to make casting decisions for a play they are producing in this voting system, voter A has a weight of 5, voter B has a weight of 4 voter C has a weight of 3, and voter D has a weight of 2.

Concept used:

BPI(v)=number of times voter v is a critical voternuner of times any voter is a critical voter

Calculation:

Consider four staff members A,B,C and D and the weighted system is {8:5,4,3,2}.

Therefore,

 Winning coalition Number of votes Critical voters {A,B} 9 {A,B} {A,C} 8 {A,C} {A,B,C} 12 {A} {A,B,D} 11 {A,B} {A,C,D} 10 {A,C} {B,

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