   # Music Education A music department Consists of a hand director and a music teacher. Decisions on motions are made by voting. If both members vote in favor of a motion, it passes. If both members vote against a motion. It fails. In the event of a tie vote, the principal of the school votes to break the tie. For this voting scheme. Determine the Banzhaf power index for each department member and for the principa!. Hint: See Example 3, page 214. ### 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 15ES
Textbook Problem
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## Music Education A music department Consists of a hand director and a music teacher. Decisions on motions are made by voting. If both members vote in favor of a motion, it passes. If both members vote against a motion. It fails. In the event of a tie vote, the principal of the school votes to break the tie. For this voting scheme. Determine the Banzhaf power index for each department member and for the principa!. Hint: See Example 3, page 214.

To determine

Determine the Banzhaf power index for each department member and for the principal. Hint: See Example 3 ,page 217.

### Explanation of Solution

Given Information:

Music Education: A music department consists of a band director and a music teacher.

Decisions on motions are made by voting. If both members vote in favor of a motion, it passes. If both members vote against a motion, it fails. In the event of a tie vote, the principal of the school votes to break the tie.

Concept used:

BPI(v)=Number of times voter v is a critical voterNuner of times any voter is a critical voter

Calculation:

Consider A for bad director and B for music teacher and P is for principle

 Winning Coalition(Without principal) Critical voters Winning Coalition(Without Voting) Critical Voters {A,B} {A,B} {A,P} {A,P} {B,P} {B,P}

By examining the table, we see that A,BandP each occur in exactly 2 winning coalition

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