Exercise
There is an election with 27 voters and 3 candidates: Alejandro (A), Baobao (B), and Corrina (C).
| Number of Voters | 7 | 6 | 5 | 3 | 3 | 3 |
|---|---|---|---|---|---|---|
| 1st | A | B | C | A | B | C |
| 2nd | C | C | B | B | A | A |
| 3rd | B | A | A | C | C | B |
- Who would win using (basic) plurality?
- Who would win using a Borda count?
- Who would win using plurality with elimination?
- Who would win using pairwise comparison?
- Which of the four methods do think does a better job of choosing the winner of this election? Why?
Exercise
There is an election with 9 voters and 3 candidates: Amber (A), Bernard (B), and Crystal (C). Ties are common with the pairwise comparison method. Complete the ballots below so that each candidate wins exactly one of the one-on-one comparisons. This means they all tie for 1st place using the pairwise comparison method, so how would you decide a winner?
| Ranking | Ballot | Ballot | Ballot | Ballot | Ballot | Ballot | Ballot | Ballot | Ballot |
|---|---|---|---|---|---|---|---|---|---|
| 1st | A | A | A | A | B | B | C | C | C |
| 2nd | |||||||||
| 3rd |
Exercise
- In a couple of sentences, explain why the pairwise comparison method satisfies the Condorcet criterion. (See Handout 02.)
- In a couple of sentences, explain why the pairwise comparison method satisfies the majority criterion. (See Handout 03.)