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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 4.3, Problem 23ES

Textbook Problem

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Football At the beginning of each football season, the coaching staff at Vista High School must vote to decide which players to select for the team. They use the weighted voting system {4: 3. 2. 1). In this voting system, the head coach. A. has a weight of 3, the assist ant coach. B. has a weight of 2, and the junior varsity coach. C. has a weight of I.

a. Compute the Banzhaf power index for each of the coaches.

b. Explaintiy it seems reasonable that the assisant coach and the junior varsity coach have the same Banzhaf power index in this voting system.

To determine

**(a)**

Compute the Banzhaf power index for each of the coaches.

**Given Information:**

Consider three people the head coach,

**Concept used:**

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**Calculation:**

In above table we look in Critical voters column and find that

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Then

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To determine

**(b)**

Explain why it seems reasonable that the assistant coach and the junior varsity coach have the same Banzhaf power index in this voting system.

Mathematical Excursions (MindTap Course List)

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