Answer
Before Candidate C drops out, Candidate B was selected as the winner using the Borda count method. After one of the losing candidates, Candidate C, drops out, Candidate B was again selected as the winner using the Borda count method. Therefore, the irrelevant alternatives criterion is satisfied.
Work Step by Step
With the Borda count method, each candidate receives 1 point for each last place vote, 2 points for each second-to-last-place vote, and so on. The candidate with the most points is declared the winner.
We can find the total points for each candidate before Candidate C drops out.
Candidate A:
3(400) + 2(0) + 1(250 + 200) = 1650 points
Candidate B:
3(200) + 2(400 + 250) + 1(0) = 1900 points
Candidate C:
3(250) + 2(200) + 1(400) = 1550 points
Since Candidate B received the most points using the Borda count method, Candidate B wins the election.
After Candidate C drops out, we can go through the Borda count method again. Note that every candidate below Candidate C on a ballot moves up one spot on that ballot.
We can find the total points for each candidate.
Candidate A:
2(400) + 1(250 + 200) = 1250 points
Candidate B:
2(250 + 200) + 1(400) = 1300 points
Since Candidate B received the most points using the Borda count method, Candidate B wins the election.
Before Candidate C drops out, Candidate B was selected as the winner using the Borda count method. After one of the losing candidates, Candidate C, drops out, Candidate B was again selected as the winner using the Borda count method. Therefore, the irrelevant alternatives criterion is satisfied.
