Answer
(a) Candidate B is declared the winner using the Borda count method.
(b) The majority criterion is not satisfied. Candidate A has a majority of the first-place votes but Candidate A was not declared the winner of the election.
Work Step by Step
(a) With the Borda count method, each candidate receives 1 point for each fourth-place vote, 2 points for each third-place vote, 3 points for each second-place vote, and 4 points for each first-place vote. The candidate with the most points is declared the winner.
We can find the total points for each candidate.
Candidate A:
4(20) + 3(0) + 2(0) + 1(15 + 3 + 1) = 99 points
Candidate B:
4(15) + 3(20 + 1) + 2(3) + 1(0) = 129 points
Candidate C:
4(3) + 3(15) + 2(20 + 1) + 1(0) = 99 points
Candidate D:
4(1) + 3(3) + 2(15) + 1(20) = 63 points
Since Candidate B received the most points, Candidate B is declared the winner using the Borda count method.
(b) The total number of votes in this election is 20 + 15 + 3 + 1 which is 39.
Candidate A has 20 first-place votes which is more than half of the total votes in this election. Therefore, Candidate A has a majority of first-place votes.
The majority criterion is not satisfied. Candidate A has a majority of the first-place votes but Candidate A was not declared the winner of the election.