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Ask voters to rank in order of preference
Voter's Preferences are......
In an election with n candidates, the largest possible # of columns in preference schedule is
Voting Method: cadidate with most first choice votes wins
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.
- 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 head-to-head comparison, then x should be the winnder.
- -called the "condorcet candidate"
- - If x is winner of an election and in a re-election 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 non-winner of an election withdraws or is disqualified, then x should still win.
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
- head-to-head 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