MA 111 Voting Methods

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

  4. Voting Method: cadidate with most first choice votes wins
    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:
  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
    • 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
  17. Pros of Method of Pairwise Comparison
    Satisfies condorcet criterion, monotonicity, and majority criterion.
  18. Cons of Method of Pairwise Comparison
    Violates IIA
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MA 111 Voting Methods
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