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