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?

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

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

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?

Plurality with Elimination

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.

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.

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.

Voting Classwork

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?

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