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.

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

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

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

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.

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?

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

This violates the Monotonicity Criterion.

Is it fair? – Pairwise Comparison

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.