(a) Explanation Given: The preference table shows the results of the election. Number of Votes 6 4 3 1 1 1 First W C C F F W Second A A W W C F Third C W F A W C Fourth F F A C A A The following choices are Chronicles of Narnia (C), Family Classic (F), Anne of Green Gables (A) and Where on Earth Is Sandiego (W). Voting method use: Plurality-with-elimination method: 1. Each voter votes for one candidate. 2. If a candidate receives a majority of votes, that candidate is declared the winner of the election. 3. If no candidate receives a majority, eliminate the candidate with the fewest votes and hold another election (if there is a tie for the fewest votes, eliminate all candidates tied for the fewest votes). 4. Repeat this process until a candidate receives a majority. Calculation: The total number of votes is 16, means that the majority out of 16 votes is 9 or more votes. Now, first count the number of first place votes for each DVD set. The first place votes for DVD (W) are equal to 7, DVD (A) is equal to 0, the DVD (C) is equal to 7 and the DVD (F) is equal to 2. To receive a majority, a candidate should receive more than half of the votes. That is, out of 16 votes 9 or more votes to receive a majority. In this election no DVD set out of four received a majority. Since the DVD set (A) received the fewest number of first- place votes (0 votes only), it is eliminated in the first round... (b) To determine The DVD set which is chosen by using Borda Count Method. (c) To determine The DVD set which is chosen if the staff members are agree to break a tie using the pair-wise comparison method.

A Survey of Mathematics with Applications plus MyLab Math Student Access Card -- Access Code Card Package (10th Edition)

10th Edition

ISBN: 9780134115764

Author: Allen R. Angel, Christine D. Abbott, Dennis Runde

Publisher: PEARSON

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Chapter 14, Problem 19RE

(a)

To determine

The DVD set which is selected using the plurality-with-elimination method.

(b)

To determine

The DVD set which is chosen by using Borda Count Method.

(c)

To determine

The DVD set which is chosen if the staff members are agree to break a tie using the pair-wise comparison method.

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Chapter 14, Problem 18RE

Chapter 14, Problem 20RE

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Chapter 14 Solutions

A Survey of Mathematics with Applications plus MyLab Math Student Access Card -- Access Code Card Package (10th Edition)

Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - Prob. 5E Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Plurality Three candidates are running for mayor...Ch. 14.1 - Prob. 10E

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The DVD set which is selected using the plurality-with-elimination method.

Solution Summary: The author explains the plurality-with-elimination method used to determine the winner of the election.

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The DVD set which is selected using the plurality-with-elimination method.

The DVD set which is chosen by using Borda Count Method.

The DVD set which is chosen if the staff members are agree to break a tie using the pair-wise comparison method.

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Chapter 14 Solutions