   # In the following exercises that involve weighted voting systems for voters A. B. C. ... the systems are given in the form { q : w 1 , w 2 , w 3 , w 4 , ... , w n } . The weight of voter A is w 1 . the weight of voter B is w 2 . the weight of voter C is w 3 , and so on. A weighted voting system is given by { 16 : 8 , 7 , 4 , 2 , 1 } . a. What is the quota? b. How many voters are in this system? c. What is the weight of voter C? d. What is the weight of the coalition { B , C } )? e. Is { B , C , D , E } a winning coalition? I. Which voters are critical voters in the coalition { A , B , D } ? g. How many coalitions can be formed? h. How many coalitions consist of exactly three 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 4.3, Problem 2ES
Textbook Problem
10 views

## In the following exercises that involve weighted voting systems for voters A. B. C. ... the systems are given in the form { q : w 1 , w 2 , w 3 , w 4 , ... , w n } . The weight of voter A is w 1 . the weight of voter B is w 2 . the weight of voter C is w 3 , and so on.A weighted voting system is given by { 16 : 8 , 7 , 4 , 2 , 1 } .a. What is the quota?b. How many voters are in this system?c. What is the weight of voter C?d. What is the weight of the coalition { B , C } )?e. Is { B , C , D , E } a winning coalition?I. Which voters are critical voters in the coalition { A , B , D } ?g. How many coalitions can be formed?h. How many coalitions consist of exactly three voters? To determine

(a)

To determine the quota of the weighted voting system {16:8,7,4,2,1}

### Explanation of Solution

Given information:

{16:8,7,4,2,1}

The number of votes that are required to pass the measure is called the Quota

To determine

(b)

To determine the number of voters in the weighted voting system {16:8,7,4,2,1}

To determine

(c)

To determine the weight of voter C in the weighted voting system {16:8,7,4,2,1}

To determine

(d)

To determine the weight of the coalition {B,C} in the weighted voting system {16:8,7,4,2,1}

To determine

(e)

To determine whether {B,C,D,E} is a winning coalition in the weighted voting system {16:8,7,4,2,1}

To determine

(f)

To determine which voters are critical voters in the coalition {A,B,D}

To determine

(g)

To determine how many coalitions can be formed from the weighted voting system {16:8,7,4,2,1}

To determine

(h)

To determine how many coalitions consist of exactly three voters in the weighted voting system {16:8,7,4,2,1}

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