#### Answer

Candidate A wins the election using the pairwise comparison method.

#### Work Step by Step

With the pairwise comparison method, each candidate is compared with every other candidate. For each pair of candidates, if one candidate is ranked higher than the other candidate on a majority of ballots, then the higher-ranked candidate receives 1 point. If the two candidates tie, then they each receive 0.5 points. After all of the comparisons have been made, the candidate who receives the most points is declared the winner.
We can compare Candidate A and Candidate C. We can find the number of ballots with Candidate A ranked higher than Candidate C and the number of ballots with Candidate C ranked higher than Candidate A.
Candidate A: 180 + 100 = 280
Candidate C: 40 + 30 = 70
Since Candidate A is ranked higher than Candidate C on more ballots, Candidate A receives 1 point.
We can compare Candidate A and Candidate B. We can find the number of ballots with Candidate A ranked higher than Candidate B and the number of ballots with Candidate B ranked higher than Candidate A.
Candidate A: 180
Candidate B: 100 + 40 + 30 = 170
Since Candidate A is ranked higher than Candidate B on more ballots, Candidate A receives 1 point.
We can compare Candidate B and Candidate C. We can find the number of ballots with Candidate B ranked higher than Candidate C, and the number of ballots with Candidate C ranked higher than Candidate B.
Candidate B: 180 + 100 + 40 = 320
Candidate C: 30
Since Candidate B is ranked higher than Candidate C on more ballots, Candidate B receives 1 point.
We can compare Candidate A and Candidate D. We can find the number of ballots with Candidate A ranked higher than Candidate D and the number of ballots with Candidate D ranked higher than Candidate A.
Candidate A: 180 + 30 = 210
Candidate D: 100 + 40 = 140
Since Candidate A is ranked higher than Candidate D on more ballots, Candidate A receives 1 point.
We can compare Candidate D and Candidate C. We can find the number of ballots with Candidate D ranked higher than Candidate C and the number of ballots with Candidate C ranked higher than Candidate D.
Candidate D: 100 + 40 = 140
Candidate C: 180 + 30 = 210
Since Candidate C is ranked higher than Candidate D on more ballots, Candidate C receives 1 point.
We can compare Candidate B and Candidate D. We can find the number of ballots with Candidate B ranked higher than Candidate D and the number of ballots with Candidate D ranked higher than Candidate B.
Candidate B: 180 + 100 + 30 = 310
Candidate D: 40
Since Candidate B is ranked higher than Candidate D on more ballots, Candidate B receives 1 point.
After all of the pairwise comparisons have been made, we can add up the total number of points for each candidate.
Candidate A: 1 + 1 + 1 = 3 points
Candidate B: 1 + 1 = 2 points
Candidate C: 1 point
Candidate D: 0 points
Since Candidate A received the most points, Candidate A is declared the winner.
Candidate A wins the election using the pairwise comparison method.