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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?

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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

Solutions

Chapter
Section
BuyFindarrow_forward

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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Chapter 4 Solutions

Mathematical Excursions (MindTap Course List)
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Ch. 4.1 - Sales Associates The table below shows the number...Ch. 4.1 - Hospital Interns The table below shows the number...Ch. 4.1 - House of Representatives The U.S. House of...Ch. 4.1 - College Enrollment The following table shows the...Ch. 4.1 - Medical Care A hospital district consists of six...Ch. 4.1 - What is the Alabama paradox?Ch. 4.1 - What is the population paradox?Ch. 4.1 - What is the new states paradox?Ch. 4.1 - 15. 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What method is presently used to apportion the...Ch. 4.1 - 32. According to the 2010 census, what is the...Ch. 4.1 - John Quincy Adams, the sixth president of the...Ch. 4.1 - In the Huntington-Hill method of apportionment,...Ch. 4.1 - Deriving the Huntington-Hill Number The...Ch. 4.2 - Using the Borda method of voting, which flavor of...Ch. 4.2 - Instead of using the normal Borda method, suppose...Ch. 4.2 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Suppose the Borda method used in Exercise 1 of...Ch. 4.2 - Can the assignment of points for first. Second,...Ch. 4.2 - Suppose the assignment of points for first,...Ch. 4.2 - What is the difference between a majority and a...Ch. 4.2 - Explain why the plurality voting system may not be...Ch. 4.2 - Explain how the Borda Count method of voting...Ch. 4.2 - Explain how the plurality with elimination voting...Ch. 4.2 - 5. Explain how the pairwise comparison voting...Ch. 4.2 - What does the Condorcet criterion say?Ch. 4.2 - Is there a best voting method? Is one method more...Ch. 4.2 - Explain why. if only two candidates are running,...Ch. 4.2 - Presidential Election The table below shows the...Ch. 4.2 - Breakfast Cereal Sixteen people were asked to rank...Ch. 4.2 - Cartoon Characters A kindergarten class was...Ch. 4.2 - Catering A 15-person committee is having lunch...Ch. 4.2 - Movies Fifty consumers were surveyed about their...Ch. 4.2 - Breakfast Cereal Use the Borda count method of...Ch. 4.2 - Cartoons Use the Borda count method of voting to...Ch. 4.2 - Catering Use the Borda count method of voting to...Ch. 4.2 - Class Election A senior high school class held an...Ch. 4.2 - Cell Phone Usage A journalist reviewing various...Ch. 4.2 - Baseball Uniforms A Little League baseball team...Ch. 4.2 - Radio Stations A number of college students were...Ch. 4.2 - Class Election Use plurality with elimination to...Ch. 4.2 - Cell Phone Usage Use plurality with elimination to...Ch. 4.2 - Campus Club A campus club has money left over in...Ch. 4.2 - Recreation A company is planning its annual summer...Ch. 4.2 - X-Men Movies Fans of the X-Men movies have been...Ch. 4.2 - Family Reunion The Nelson family is trying to...Ch. 4.2 - School Mascot A new college needs to pick a moscot...Ch. 4.2 - Election Five candidates are running for president...Ch. 4.2 - Baseball Uniforms Use the pairwise comparison...Ch. 4.2 - Radio Stations Use the pairwise comparison method...Ch. 4.2 - Does the winner in Exercise tic satisfy the...Ch. 4.2 - 32. Does the winner in Exercise 12 satisfy the...Ch. 4.2 - Does the winner in Exercise 2k satisfy the...Ch. 4.2 - Does the winner in Exercise 24c satisfy the...Ch. 4.2 - Does the winner in Exercise 17 satisfy the...Ch. 4.2 - Does the winner in Exercise 20 satisfy the...Ch. 4.2 - Election Three candidates are running for mayor. A...Ch. 4.2 - Film Competition Three films have been selected as...Ch. 4.2 - 39. Election A campus club needs to elect four...Ch. 4.2 - Scholarship Awards The members of a scholarship...Ch. 4.2 - Another method of voting is to assign a weight. or...Ch. 4.2 - Approval voting is a system in which voters may...Ch. 4.2 - Restaurants Suppose you and three friends. David,...Ch. 4.3 - Using the data in Example 1 on page 211, list all...Ch. 4.3 - For the data in Example I on page 211, calculate...Ch. 4.3 - Using the data in Check Your Progress 3 on page...Ch. 4.3 - For the data in Check Your Progress 3 on page 215,...Ch. 4.3 - Create a voting system with three members that is...Ch. 4.3 - Create a voting system with four members in which...Ch. 4.3 - Create a voting system with five members that...Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Which, if any, of the voting systems in Exercises...Ch. 4.3 - Explain why it is impossible to calculate the...Ch. 4.3 - Music Education A music department Consists of a...Ch. 4.3 - Four voters. 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