   # A weighted voting system for voters A, B, C, D. and E is given by { 33 : 21 , 14 , 12 , 7 , 6 } . a. What is the quota? b. What is the weight of the coalition { B,C } ? c. Is { B,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 4T
Textbook Problem
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## A weighted voting system for voters A, B, C, D. and E is given by { 33 : 21 , 14 , 12 , 7 , 6 } .a. What is the quota?b. What is the weight of the coalition { B,C } ?c. Is { B,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)

What is the quota?

### Explanation of Solution

Given Information:

A weighted voting system for voters A,B,C,D and E is given by {33:21,14,12,7,6}.

Concept used:

Quota is the optimum value in weighted voted system

To determine

(b)

What is the weight of the coalition {B,C} ?

To determine

(c)

Is {B,C} a winning coalition?

To determine

(d)

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

To determine

(e)

How many coalitions can be formed?

To determine

(f)

How many coalitions consist of exactly two voters?

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