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Ask voters to rank in order of preference
Preference ballots

Voter's Preferences are......
transitive

In an election with n candidates, the largest possible # of columns in preference schedule is
n!
1x2x3x4......=n!

Voting Method: cadidate with most first choice votes wins
Plurality Method

Pros of Plurality Method
  Simplicity
  Majority of people get what they want

Cons of Plurality Method
Just because candidate has most first place votes, doesnt mean that most voters will be happy with decision.


Fairness Criteria
 Majority Criteria
  If x has majority, then x should be the winner.
  Plurality method satisfies majority criterion, since any candidate with majority has plurality.
 The Condorcet Criterion
 If x is preferred by voters over each of the other candidates in a headtohead comparison, then x should be the winnder.
 called the "condorcet candidate"
 Monotonicity
  If x is winner of an election and in a reelection the only changes in the ballots favor x and only x, then x should remain the winner.
 Independence of Irrelevant Alternatives (IIA)
  If x is winner, and a nonwinner of an election withdraws or is disqualified, then x should still win.

Insincere/strategic voting
when voters know when their candidate won't win the election, so they vote for a more popular candidate.
Ex: Independent candidates in a presidential election
*can dramatically impact the result of an election using the plurality method.

Borda Count Method
 In an election with n candidates, we give 1 point for last place vote, 2 points for second to last place, etc and n points for first place.
  Tally points for each candidate.
  Candidate with most points wins.

Pros of Borda Count Method
 takes all voters' preferences into account.
 gives best compromise candidate

Cons of Borda Count Method
 can violate Majority and Condorcet criteria (relatively rare)
 overall still one of the best

Plurality with Elimination Method
 1. Count # of 1st place vots for each candidate
 if one candidate has the majority of votes, they are the winner. Done
 If there isn't a clear majority, eliminate candidate with fewest 1st place votes.
 cross out eliminated candidates and rewrite preference schedule by moving up remaining candidate as appropriate
 if candidate has majority of votes now, they win. Done.

Pros of PwEM
always satisfies majority criterion

Cons of PwEM
 violates Monotonicity
 also possible to violate condorcet criterion

The Method of Pairwise Comparison
 headtohead matchup between 2 candidates
 whichever candidate is ranked higher by the most voters was the pairwise comparison
 1. Do pairwise comparison of each pair of candidates
 2. The winner of each pariwise comparison gets 1 point, loser gets 0. Tie gets 1/2
 3. Candidate with most points wins

Pros of Method of Pairwise Comparison
Satisfies condorcet criterion, monotonicity, and majority criterion.

Cons of Method of Pairwise Comparison
Violates IIA

