1. Quiz – 1/24 - Friday How many people voted in the election?
Using the plurality method, who wins the
Election?
3. Determine a winner using a second method.
State the method that you used and the winner.

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

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

4. Is it fair? - Plurality Method
The plurality method fails the Condorcet Criterion.
In the table to the right A has the most first place votes.
However, B is the preferred candidate
B: 55 voters vs. A: 51 voters

5. Is it fair? – Borda Count
Using the Borda Count method, B would win this election.
This clearly violates the majority criterion as A received the most first place votes.

6. Is it fair? – Plurality with Elimination
If we use Plur-w/Elim to the schedule on the right, C is the winner.
What happens if those 4 voters who voted for A switched to C?

7. Is it fair? – Plurality with Elimination
C won the first election.
In election 2, C gains 4 first place votes from A.
Who wins?

8. This violates the Monotonicity Criterion.

9. Is it fair? – Pairwise Comparison

11. 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.