   # A weighted voting system for voters A. B. C. D. and E is given by { 36 : 29 , 11 , 8 , 4 , 2 } . The weight of voter A is 29, the weight of voter B is 11, the weight of voter C is 8, the weight of voter D is 4, and the weight of voter E is 2. a. What is the quota? b. What is the weight of the coalition { A, D, E } ? c. Is { A, D, E } a winning coalition? d. Which voters are critical voters in the coalition { A, C, D, E } e. How many coalitions can be formed? f. How many coalitions consist of exactly two voters? ### 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 22RE
Textbook Problem
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## A weighted voting system for voters A. B. C. D. and E is given by { 36 : 29 , 11 , 8 , 4 , 2 } . The weight of voter A is 29, the weight of voter B is 11, the weight of voter C is 8, the weight of voter D is 4, and the weight of voter E is 2.a. What is the quota?b. What is the weight of the coalition { A, D, E } ?c. Is { A, D, E } a winning coalition?d. Which voters are critical voters in the coalition { A, C, D, E } e. How many coalitions can be formed?f. How many coalitions consist of exactly two voters?

To determine

(a)

To define:

quota for the given voting system.

### Explanation of Solution

Given information:

A weighted voting system for voters A, B, C, D and E is given by {35:29,11,8,4,2}

To determine

(b)

To find:

The weight of the coalition {A,D,E}.

To determine

(c)

To check:

The weight of the coalition {A,D,E} is winner.

To determine

(d)

To find:

Critical voters

To determine

(e)

To find:

Number of coalitions formed.

To determine

(f)

To find:

Number of coalitions formed exactly two voters.

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