1. Warm Up – 5/27 - Monday How many people voted in the election?
Using the Plurality Method, who wins the election?
Who wins the election using the Borda Count Method?

2. Final Exam Unit 1: Voting
Four methods: Plurality, Borda Count, Plurality w/Elimination, Pairwise Comparisons
Fairness Criterion
Weighted Voting
Banzhaf Power Index

3. Examples Plurality: Most government elections… Borda Count:
Sports Rankings/Awards

5. Example #1 How many voters are there? How many votes would be
Needed for a majority (50%)?
Does anyone have 50%
or more of the vote?

7. Plurality with Elimination

9. Condorcet Candidates
A Condorcet Candidate is a candidate who would win an a pairwise comparison against all other candidates.
Condorcet Candidates always win elections when using the method of pairwise comparisons.

10. Fairness Criterion
We want to make our elections fair. There are 4 criterion that make an election fair.

11. In other words, a voter should not be able to hurt
the winner by moving him/her up in his ballot.

12. Arrow’s Impossibility Theorem
Mathematician Kenneth Arrow tells us this simple truth: NO ELECTION IS FAIR.
No election involving more than two candidates can satisfy all four of the fairness criterion.

13. Voting Classwork

14. Weighted Voting Consider the following voting system.
[12:5, 4, 3, 2, 1]
What is the quota?
Is there a dictator?
Are there any dummies?
D) Do any players have veto power?

15. Step 1: Write out winning coalitions
Step 2: Determine critical players (If the player is removed will the coalition still win?)
Step 3: Find total number of critical players.
Step 4: Count number of times each individual player is critical.
Step 5: 𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝑡𝑜𝑡𝑎𝑙 =𝛽