# MA 111 Voting Methods

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1. Ask voters to rank in order of preference
Preference ballots
2. Voter's Preferences are......
transitive
3. In an election with n candidates, the largest possible # of columns in preference schedule is
n!

1x2x3x4......=n!
Plurality Method
5. Pros of Plurality Method
• - Simplicity
• - Majority of people get what they want
6. Cons of Plurality Method
-Just because candidate has most first place votes, doesnt mean that most voters will be happy with decision.
7. Over 1/2 voted:
Majority
8. 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 head-to-head comparison, then x should be the winnder.
• -called the "condorcet candidate"

• Monotonicity
• - 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.
9. 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.
10. 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.
11. Pros of Borda Count Method
• -takes all voters' preferences into account.
• -gives best compromise candidate
12. Cons of Borda Count Method
• -can violate Majority and Condorcet criteria (relatively rare)
• -overall still one of the best
13. 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.
14. Pros of PwEM
always satisfies majority criterion
15. Cons of PwEM
• -violates Monotonicity
• -also possible to violate condorcet criterion
16. The Method of Pairwise Comparison
• -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
17. Pros of Method of Pairwise Comparison
Satisfies condorcet criterion, monotonicity, and majority criterion.
18. Cons of Method of Pairwise Comparison
Violates IIA

## Card Set Information

 Author: CarsonRhea ID: 131759 Filename: MA 111 Voting Methods Updated: 2012-01-30 22:36:44 Tags: Exam Folders: Description: Vocab and practice Show Answers:

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