QuestionCandidates , , and are running for mayor. Based on the votes, who wins using pairwise comparison?
Studdy Solution
STEP 1
Assumptions1. The number of votes are given as80,000,90,000,130,000,20,000, and30,000.
. The first choice votes go to candidates A, C, B, A, and C respectively.
3. The second choice votes go to candidates B, A, C, C, and B respectively.
4. The third choice votes go to candidates C, B, A, B, and A respectively.
5. The pairwise comparison method is used to determine the winner.
STEP 2
First, we need to calculate the total number of first choice votes for each candidate.
STEP 3
Calculate the total number of first choice votes for each candidate.
STEP 4
Now, we need to compare the votes of each pair of candidates. For each pair, the candidate with more first choice votes wins. If the first choice votes are equal, then the second choice votes are compared.
STEP 5
Compare the votes of candidates A and B.Since the first choice votes for B (130,000) are more than the first choice votes for A (100,000), B wins over A.
STEP 6
Compare the votes of candidates A and C.Since the first choice votes for C (120,000) are more than the first choice votes for A (100,000), C wins over A.
STEP 7
Compare the votes of candidates B and C.Since the first choice votes for B (130,000) are more than the first choice votes for C (120,000), B wins over C.
STEP 8
From the pairwise comparison, we can see that candidate B wins over both A and C. Therefore, candidate B becomes the new mayor.
The winner is candidate B.
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