Explanation Use plurality method, the winner of the election is as follows. The first place votes for ( W ) : 86 votes, ( X ) : 52 + 28 = 80 votes, ( Y ) : 60 votes, and ( Z ) : 58 votes. Here (W) received the most of 86 first-place plurality votes. Therefore, (W) wins with plurality of 86 votes. Similarly, use the Borda count method to find the winner of the election. Use preference table, to obtain the total award points of (W). The 86 first- place votes produce 86 × 4 = 344 points, 0 second- place votes produce 0 × 3 = 0 points. Similarly, 52 third- place votes producing 52 × 2 = 104 points and 146 fourth- place votes gives 146 × 1 = 146 points. Thus, the (W) gets 344 + 104 + 146 = 594 points. Similarly, obtain the total award points of (Y). The 60 first- place votes produce 60 × 4 = 240 points and 86 second- place votes gives 86 × 3 = 258 points. Similarly, 58 + 28 = 86 third- place votes gives 86 × 2 = 172 points, 52 fourth- place votes produce 52 × 1 = 52 points. Thus, the (Y) gets 240 + 258 + 172 + 52 = 722 points. The total award points of (Z), The 58 first- place votes gives 58 × 4 = 232 points, 52 + 28 = 80 second- place votes produce 80 × 3 = 240 points. Similarly, 86 + 60 = 146 third- place votes gives 146 × 2 = 292 points, 0 fourth- place votes produce 0 × 1 = 0 points. Thus, the (Z) gets 232 + 240 + 292 = 764 points. Obtain the total award points of (X). The 52 + 28 = 80 first- place votes produce 80 × 4 = 320 points, 118 second- place votes produce 118 × 3 = 354 points and 0 third- place votes produce 0 × 2 = 0 points

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 12T

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To explain: The voting methods of plurality, Borda count, plurality with elimination, or pair-wise comparison which violates the head-to-head criterion using the following election data.

Number of votes 86 60 58 52 28
First W Y Z X X
Second Y X X Z Z
Third Z Z Y W Y
Fourth X W W Y W

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Chapter 14, Problem 11T

Chapter 14, Problem 13T

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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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Number of votes	86	60	58	52	28
First	W	Y	Z	X	X
Second	Y	X	X	Z	Z
Third	Z	Z	Y	W	Y
Fourth	X	W	W	Y	W

The voting methods of plurality, Borda count, plurality with elimination, or pair-wise comparison which violates the head-to-head criterion using the following election data. Number of votes 86 60 58 52 28 First W Y Z X X Second Y X X Z Z Third Z Z Y W Y Fourth X W W Y W

Solution Summary: The author explains the voting methods of plurality, Borda count, pluralities with elimination, or pair-wise comparison, which violates the head-to-head criterion.

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To explain: The voting methods of plurality, Borda count, plurality with elimination, or pair-wise comparison which violates the head-to-head criterion using the following election data. Number of votes8660585228FirstWYZXXSecondYXXZZThirdZZYWYFourthXWWYW

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Chapter 14 Solutions

To explain: The voting methods of plurality, Borda count, plurality with elimination, or pair-wise comparison which violates the head-to-head criterion using the following election data.

Number of votes 86 60 58 52 28
First W Y Z X X
Second Y X X Z Z
Third Z Z Y W Y
Fourth X W W Y W