   # 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 { 6 : 4 , 3 , 2 , 1 } . a. What is the quota? b. How many voters are in this system? c. What is the weight of voter B? d. What is the weight of the coalition { A , C } ? e. Is { A , D } a winning coalition? f. Which voters are critical voters in the coalition { A , C , D } ? g. I-low many coalitions can be formed? h. 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 4.3, Problem 1ES
Textbook Problem
3 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 { 6 : 4 , 3 , 2 , 1 } .a. What is the quota?b. How many voters are in this system?c. What is the weight of voter B?d. What is the weight of the coalition { A , C } ?e. Is { A , D } a winning coalition?f. Which voters are critical voters in the coalition { A , C , D } ?g. I-low many coalitions can be formed?h. How many coalitions consist of exactly two voters?

To determine

(a)

Weighted voting system is given by {6:4,3,2,1}.

### Explanation of Solution

Given Information:

A weighted voting system is given by {6:4,3,2,1}.

Concept used:

The weight of voter A is w1, the weight of voter B is w2<

To determine

(b)

How many voters are in this system?

To determine

(c)

What is the voter B.

To determine

(d)

What is the weight of tile coalition {A,C} ?

To determine

(e)

Is {A,D} a winning coalition?

To determine

(f)

Which voters are critical voters in the coalition {A, C, D}

To determine

(g)

How many coalitions can be formed?

To determine

(h)

How many coalitions consist of exactly two voters?

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