Question

number of voters 6 12 14
1st choice b c a
2nd choice c b b
3rd choice a a c
find the winner of this election under the pairwise comparison method (copelands method).
winner =

Explanation:

Step1: Identify all pairs

We have three candidates: A, B, C. The pairs are (A vs B), (A vs C), (B vs C).

Step2: Compare A and B

• For A vs B:
• Voters who prefer A over B: The group with 1st choice A (14 voters). Also, check 2nd and 3rd choices. Wait, in pairwise comparison, we look at the number of voters who rank one candidate higher than the other.
• Let's list the preferences:
• Group 1 (6 voters): 1st B, 2nd C, 3rd A → prefer B over A.
• Group 2 (12 voters): 1st C, 2nd B, 3rd A → prefer B over A (since B is 2nd, A is 3rd).
• Group 3 (14 voters): 1st A, 2nd B, 3rd C → prefer A over B.
• So number of voters preferring A over B: 14. Number preferring B over A: 6 + 12 = 18. So B wins this pair, B gets 1 point, A gets 0.

Step3: Compare A and C

• For A vs C:
• Group 1 (6 voters): 1st B, 2nd C, 3rd A → prefer C over A (C is 2nd, A is 3rd).
• Group 2 (12 voters): 1st C, 2nd B, 3rd A → prefer C over A (C is 1st, A is 3rd).
• Group 3 (14 voters): 1st A, 2nd B, 3rd C → prefer A over C (A is 1st, C is 3rd).
• Number preferring A over C: 14. Number preferring C over A: 6 + 12 = 18. So C wins this pair, C gets 1 point, A gets 0.

Step4: Compare B and C

• For B vs C:
• Group 1 (6 voters): 1st B, 2nd C, 3rd A → prefer B over C (B is 1st, C is 2nd).
• Group 2 (12 voters): 1st C, 2nd B, 3rd A → prefer C over B (C is 1st, B is 2nd).
• Group 3 (14 voters): 1st A, 2nd B, 3rd C → prefer B over C (B is 2nd, C is 3rd).
• Number preferring B over C: 6 + 14 = 20. Number preferring C over B: 12. So B wins this pair, B gets 1 point, C gets 0.

Step5: Tally points

• A: 0 points
• B: 1 (from A vs B) + 1 (from B vs C) = 2 points
• C: 1 (from A vs C) point

Since B has the highest number of points (2), B is the winner.

Answer:

B