Math of Elections #7

Pairwise Comparison Method (continued)

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
  1. Who would win using (basic) plurality?



  2. Who would win using a Borda count?




  3. Who would win using plurality with elimination?




  4. Who would win using pairwise comparison?




  5. 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

  1. In a couple of sentences, explain why the pairwise comparison method satisfies the Condorcet criterion. (See Handout 02.)









  2. In a couple of sentences, explain why the pairwise comparison method satisfies the majority criterion. (See Handout 03.)