   # A weighted voting system for voters A, B, C, and D is given by { 18 : 12 , 7 , 6 , 1 } . The weight of voter A is 12, the weight of voter B is 7, the weight of voter C is 6, and the weight of voter D is 1. a. What is the quota? b. What is the weight of the coalition { A , C } ? c. Is { A , C } a winning coalition? d. Which voters are critical voters in the coalition { A , C , D } ? 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 21RE
Textbook Problem
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## A weighted voting system for voters A, B, C, and D is given by { 18 : 12 , 7 , 6 , 1 } . The weight of voter A is 12, the weight of voter B is 7, the weight of voter C is 6, and the weight of voter D is 1.a. What is the quota?b. What is the weight of the coalition { A , C } ?c. Is { A , C } a winning coalition?d. Which voters are critical voters in the coalition { A , C , D } ?e. How many coalitions can be formed?f. How many coalitions consist of exactly two voters?

To determine

(a)

To define:

The quota for the given voting system.

### Explanation of Solution

Given information:

A weighted voting system for voters A, B, C and D is given by {18:12,7,6,1}

To determine

(b)

To find:

The weight of the coalition {A,C}.

To determine

(c)

Is the weight of the coalition {A,C} is winner?

To determine

(d)

To find:

Critical voters for the mentioned voting system.

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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