1. 1.1, 1.2 Ballots and Plurality Method

2. Preference Ballot: a ballot in which voters are asked to rank the candidates in order

3. Preference Schedule: a table that organizes the ballots
Number of voters 14 10 8 4 1
1st choice A C D B
2nd choice
3rd choice
4th choice

4. Transitivity and Elimination
A voter prefers A over B and B over C means she prefers A over C
If a candidate drops out, others can move up

5. The Plurality Method: if X has the most first-place votes, then X is the winner.
A is the winner with 14 votes
R is the winner with 49 votes

6. First basic fairness criterion
The Majority Criterion: if X has the majority of the first-place votes (more than half), then X is the winner.
The plurality method satisfies the majority criterion.

7. Insincere voting (Strategic voting)
VOTED SINCERELY
VOTED INSINCERELY
Page 8: We know that the candidate we really want doesn’t have a chance of winning, so we can cast it for a less choice that has a better chance of winning the election.
Page 9: Insincere voting not only hurts small parties, it has negative consequences on the political system itself. The history of American political elections is that small parties never get a fair voice or a fair level of funding because of the “let’s not waste our vote” philosophy of insincere voters.

8. Second basic fairness criterion
The Condorcet Criterion was introduced in 1785 by the French mathematician Le Marquis de Condorcet
If candidate X is preferred over other candidates in a head-to-head comparison, then X is the winner
If X is the winner under the Majority Criterion, then X is also the Condorcet winner.

9. Under the Plurality method, who is the winner. Is it fair
Under the Plurality method, who is the winner? Is it fair? Who is the winner under Condorcet Criterion?
Under head-to-head count:
R – H :
49 – 51
F – H :
03– 97
O – H :
0 – 100
S – H :
0 – 100
Therefore, H is preferred over other candidates and H is the Condorcet winner

10. Example 10 6 5 4 2 1st A B C D 2nd 3rd 4th How many candidates? 4
2) How many people voted? 27
3) Which candidate has the most first-place votes? Is it a majority or plurality?
B, Plurality
4) Does the answer in question 3 violate Majority Criterion?
No, because there is no Majority winner.
5) Is there a Condorcet candidate? If yes, find her.
Yes, C
6) Does the answer in question 3 violate the Condorcet Criterion?
Yes, because when we do head-to-head comparison, C is the winner, not B 10 6 5 4 2
1st A B C D
2nd
3rd
4th