Explanation Given: The planning committee consists of nine members. The choices A, B, and C are ranked in the preference table which is shown below. Numbers of votes 5 2 2 First C A B Second A B A Third B C C Calculation: By Borda count method, the candidate who receives the highest points is declared as the winner. For third place, A receives 0 votes that count to 0 × 1 = 0 points, B receives 5 votes that count to 5 × 1 = 5 points, and C receives ( 2 + 2 ) = 4 vote that counts to 4 × 1 = 4 point. For second place, A receives ( 5 + 2 ) = 7 votes that count to 7 × 2 = 14 points, B receives 2 votes that count to 2 × 2 = 4 points, and C receives 0 votes that count to 0 × 2 = 0 points

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Chapter 14.2, Problem 14E

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To explain: Whether the head-to-head criterion is satisfied, when the Borda count method is used to determine the winner.

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Chapter 14.2, Problem 13E

Chapter 14.2, Problem 15E

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Chapter 14 Solutions

EBK SURVEY OF MATHEMATICS WITH APPLICAT

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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Whether the head-to-head criterion is satisfied, when the Borda count method is used to determine the winner.

Solution Summary: The author explains that the head-to-head criterion is not satisfied when the Borda count method is used to determine the winner.

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To explain: Whether the head-to-head criterion is satisfied, when the Borda count method is used to determine the winner.

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Chapter 14 Solutions