Answers: Fairness Criteria Exercises

1a. candidate A

1b. Yes, candidate A

1c. candidate A

1d. Yes, candidate A

1e. candidate C

1f. No, candidate A

2a. candidate B

2b. Yes, candidate B

2c. candidate A

2d. No, candidate B

2e. candidate B

2f. Yes

3a. candidate D

3b. candidate C

3c. Yes, candidate C

4a. candidate C

4b. candidate B

5a. candidate B

5b. Yes

6a. candidate A

6b. No, candidate B

7.
In ‘1e’ above, candidate C wins the election (under Borda Count) but candidate A has a majority of the first place votes. THIS VIOLATES THE MAJORITY CRITERION.

8.
1st Violation: In ‘1e’ above, candidate C wins the election (under Borda Count) but candidate A wins all the one-on-one matchups with the other candidates. THIS VIOLATES THE CONDORCET CRITERION.
2nd Violation: In ‘2c’ above, candidate A wins the election (under Plurality) but candidate B wins all the one-on-one matchups with the other candidates. THIS VIOLATES THE CONDORCET CRITERION.
3rd Violation: In ‘3a’ above, candidate D wins the election (under Plurality with Elimination) but candidate C wins all the one-on-one matchups with the other candidates. THIS VIOLATES THE CONDORCET CRITERION.

9.
In ‘4a’ above, candidate C wins the election (under Plurality with Elimination). After a revote in which all vote changes were favorable to candidate C, candidate C loses the election to candidate B. THIS VIOLATES THE MONOTONICITY CRITERION.

10.
1st Violation: In ‘1e’ above, candidate C wins the election (under Borda Count). However, one of the losers (candidate B) dropping out, causes candidate C to lose to candidate A.THIS VIOLATES THE IRRELEVANT ALTERNATIVES CRITERION.
2nd Violation: In ‘2c’ above, candidate A wins the election (under Plurality). However, one of the losers (candidate C) dropping out, causes candidate A to lose to candidate B. THIS VIOLATES THE IRRELEVANT ALTERNATIVES CRITERION.
3rd Violation: In ‘6a’ above, candidate A wins the election (under Pairwise Comparisons). However, one of the losers (candidate C) dropping out, causes candidate A to lose to candidate B. THIS VIOLATES THE IRRELEVANT ALTERNATIVES CRITERION.

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