1. The Plurality Method The Borda Count Method
Notes 2 – Sections 1.2 & 1.3

2. Essential Learnings
Students will understand and be able to determine the winners of elections using the Plurality and the Borda Count Methods.

3. Plurality Method
Candidate with the most first-place votes (called the plurality candidate) wins
Don’t need each voter to rank the candidates - need only the voter’s first choice

4. Plurality Method
Vast majority of elections for political office in the United States are decided using the plurality method
Many drawbacks - other than its utter simplicity, the plurality method has little else going in its favor

5. The Math Club Election Using Plurality Method:
A gets 14 first-place votes
B gets 4 first-place votes
C gets 11 first-place votes
D gets 8 first-place votes
Winner: A (Alisha)

6. Majority Rule
In a democratic election between two candidates, the candidate with a majority (more than half) of the votes should be the winner.
More than half  greater than 50%
Majority Candidate

7. Problems with Plurality Method
Two candidates: a plurality candidate is also a majority candidate - everything works out well
Three or more candidates: there is no guarantee that there is going to be a majority candidate

8. The Math Club Election Majority of votes:
Alisha, with 14 first-place votes, had a plurality (more than any other candidate) but is not a majority candidate

9. The Majority Criterion
If candidate X has a majority of the first- place votes, then candidate X should be the winner of the election.
Under plurality method, the majority candidate is guaranteed to be the winner of the election.

10. Violations
A violation of the majority criterion occurs in an election in which there is a majority candidate but that candidate does not win the election.
If this happens, then we say that the voting method itself violates the majority criterion.

11. The Marching Band Election
Tasmania State University has a superb marching band. They are so good that this coming bowl season they have invitations to perform at five different bowl games: the Rose Bowl (R), the Hula Bowl (H), the Fiesta Bowl (F), the Orange Bowl (O), and the Sugar Bowl (S). An election is held among the 100 members of the band to decide in which of the five bowl games they will perform. A preference schedule giving the results of the election is shown.

12. The Marching Band Election

13. The Marching Band Election
Under Plurality Method:
Wait! 51 voters have the Rose Bowl as last choice!
Hula Bowl has 48 first-place votes and 52 second-place votes

14. The Marching Band Election
Head to head comparison:
Hula vs. Rose: 51 to 49
Hula vs. Fiesta: 97 to 3
Hula vs. Orange: votes for Hula
Hula vs. Sugar: votes for Hula
Hula is the best choice to represent all voters.

15. The Condorcet Criterion
If candidate X is preferred by the voters over each of the other candidates in a head-to-head comparison, then candidate X should be the winner of the election.
The Marching Band Example
The plurality method violates the Condorcet criterion.

16. Insincere Voting
The idea behind insincere voting (also known as strategic voting) is simple: If we know that the candidate we really want doesn’t have a chance of winning, then rather than “waste our vote” on our favorite candidate we can cast it for a lesser choice who has a better chance of winning the election. In closely contested elections a few insincere voters can completely change the outcome of an election.

17. The Marching Band Example
Three of the band members realize that there is no chance that their first choice, the Fiesta Bowl, can win this election, so rather than waste their votes they decide to make a strategic move and they cast their votes for the Hula Bowl by switching the first and second choices in their ballots.

18. The Marching Band Example
Hula wins 51 votes.

19. Plurality Method One of the major flaws of the plurality method:
the ease with which election results can be manipulated by a voter or a block of voters through insincere voting.

20. Consequences of Insincere Voting
Insincere voting common in real-world elections
2000 and 2004 presidential elections: Close races, Ralph Nader lost many votes - voters did not want to “waste their vote.”

21. Consequences of Insincere Voting
Independent and small party candidates never get a fair voice or fair level funding (need 5% of vote to qualify for federal funds).
Entrenched two-party system, often gives voters little real choice.

22. The Borda Count Method Each place on a ballot is assigned points
With N candidates, 1 point for last place, 2 points for second from last, and so on
First-place vote is worth N points
Tally points for each candidate separately
Candidate with highest total is winner

23. The Math Club Election
Use the Borda Count Method to determine the winner.
Num. of voters 14 10 8 4 1
1st choice – 4 pts A C D B
2nd choice – 3 pts
3rd choice – 2 pts
4th choice – 1 pt

24. The Math Club Election
Use the Borda Count Method to determine the winner.
Num. of voters 14 10 8 4 1
1st choice – 4 pts
A: 56 pts
C: 40 pts
D: 32 pts
B: 16 pts
C: 4 pts
2nd choice – 3 pts
B: 42 pts
B: 30 pts
C: 24 pts
D: 12 pts
D: 3 pts
3rd choice – 2 pts
C: 28 pts
D: 20 pts
C: 8 pts
B: 2 pts
4th choice – 1 pt
D: 14 pts
A: 10 pts
A: 8 pts
A: 4 pts
A: 1 pts

25. The Math Club Election
Wait! Wasn’t A (Alisha) the winner using the Plurality method?
The Borda winner is the candidate with the best average ranking - the “best compromise candidate”.

26. The School Principal Election
The last principal at Washington Elementary School has just retired and the School Board must hire a new principal. The four finalists for the job are Mrs. Amaro, Mr. Burr, Mr. Castro, and Mrs. Dunbar (A, B, C, and D, respectively). After interviewing the four finalists, each of the 11 school board members gets to rank the candidates by means of a preference ballot, and the Borda winner gets the job.

27. The School Principal Election
Preference schedule – Use Borda count method.
Num. of voters 6 2 3
1st A B C
2nd D
3rd
4th

28. Borda Count Method Flaws
The Borda Method violates two basic criteria of fairness:
Majority criterion
Condorcet criterion
Experts in voting theory consider the Borda Count method one of the best, if not the very best, method for deciding elections with many candidates.

29. Real Life Uses of Borda Count Method
Individual sports awards (Heisman Trophy winner, NBA Rookie of the Year, NFL MVP, etc.)
College football polls
Music industry awards
Hiring of school principals, university presidents, and corporate executives

30. Assignment
p. 31 – 32: 11, 14, 16, 17 a – c, 20, 22, 23, 25 Covered Textbooks Signed Syllabus Slip