Explanation A vote for four candidates with the following results: ( ADBC ) ( CABD ) ( BCDA ) ( DBAC ) 7 5 4 1 . Calculation: In the Hare method, each voter votes for one candidate. If a candidate receives a majority of the votes, that candidate is the winner. If no candidate receives a majority, eliminate the candidate with the fewest first-place votes and repeat the process until there is a majority candidate, who wins. For this election, the total number of voters n = 7 + 5 + 4 + 1 = 17 is odd. Hence the majority is, 17 + 1 2 = 9 . That is the candidate having 9 or more votes win. The total number of votes for the candidate A is 7 . The total number of votes for the candidate B is 4 . The total number of votes for the candidate C is 5 . The total number of votes for the candidate D is 1 . None of the candidate A, B, C and D has 9 or more votes. Hence according to majority rule, there is no candidate declared to be the first-round winner. Therefore, eliminate the candidate with the fewest number of first-place votes. The candidate D has fewest votes, so eliminate candidate D as below, ( A D BC ) ( CAB D ) ( BC D A ) ( D BAC ) 7 5 4 1 . By eliminating candidate D the votes become: ( ABC ) ( CAB ) ( BCA ) ( BAC ) 7 5 4 1 The total number of first-place votes for the candidate A is 7

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 17.CR, Problem 9CR

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The winner using the Hare method for four candidates with the following results:

(ADBC)(CABD)(BCDA)(DBAC)7541.

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Nature of Mathematics (MindTap Course List)

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The winner using the Hare method for four candidates with the following results: ( ADBC ) ( CABD ) ( BCDA ) ( DBAC ) 7 5 4 1 .

Solution Summary: The author explains the Hare method, where each voter votes for one candidate. If no candidate receives a majority, eliminate the candidate with the fewest first-place votes and repeat the process.

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The winner using the Hare method for four candidates with the following results:

(ADBC)(CABD)(BCDA)(DBAC)7541.

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Chapter 17 Solutions

The winner using the Hare method for four candidates with the following results: ( ADBC ) ( CABD ) ( BCDA ) ( DBAC ) 7 5 4 1 .

Solution Summary: The author explains the Hare method, where each voter votes for one candidate. If no candidate receives a majority, eliminate the candidate with the fewest first-place votes and repeat the process.

Concept explainers

Videos

The winner using the Hare method for four candidates with the following results: (ADBC)(CABD)(BCDA)(DBAC)7541.

Want to see the full answer?

Chapter 17 Solutions

The winner using the Hare method for four candidates with the following results:

(ADBC)(CABD)(BCDA)(DBAC)7541.