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1.1, 1.2 Ballots and Plurality Method

1.1, 1.2 Ballots and Plurality Method. Preference Ballot: a ballot in which voters are asked to rank the candidates in order. Preference Schedule: a table that organizes the ballots. A voter prefers A over B and B over C means she prefers A over C. If a candidate drops out, others can move up.

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1.1, 1.2 Ballots and Plurality Method

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  1. 1.1, 1.2Ballots and Plurality Method

  2. Preference Ballot: a ballot in which voters are asked to rank the candidates in order

  3. Preference Schedule: a table that organizes the ballots

  4. A voter prefers A over B and B over C means she prefers A over C If a candidate drops out, others can move up Transitivity and Elimination

  5. The Plurality Method: if X has the most first-place votes, then X is the winner. A is the winner with 14 votes R is the winner with 49 votes

  6. First basic fairness criterion • The Majority Criterion: if X has the majority of the first-place votes (more than half), then X is the winner. • The plurality method satisfies the majority criterion.

  7. Insincere voting (Strategic voting) VOTED SINCERELY VOTED INSINCERELY Page 8: We know that the candidate we really want doesn’t have a chance of winning, so we can cast it for a less choice that has a better chance of winning the election. Page 9: Insincere voting not only hurts small parties, it has negative consequences on the political system itself. The history of American political elections is that small parties never get a fair voice or a fair level of funding because of the “let’s not waste our vote” philosophy of insincere voters.

  8. Second basic fairness criterion • The Condorcet Criterion was introduced in 1785 by the French mathematician Le Marquis de Condorcet • If candidate X is preferred over other candidates in a head-to-head comparison, then X is the winner • If X is the winner under the Majority Criterion, then X is also the Condorcet winner.

  9. Under the Plurality method, who is the winner?Is it fair? Who is the winner under Condorcet Criterion? Under head-to-head count: R – H : 49 – 51 F – H : 03– 97 O – H : 0 – 100 S – H : 0 – 100 Therefore, H is preferred over other candidates and H is the Condorcet winner

  10. Example • How many candidates? 4 2) How many people voted? 27 3) Which candidate has the most first-place votes? Is it a majority or plurality? B, Plurality 4) Does the answer in question 3 violate Majority Criterion? No, because there is no Majority winner. 5) Is there a Condorcet candidate? If yes, find her. Yes, C 6) Does the answer in question 3 violate the Condorcet Criterion? Yes, because when we do head-to-head comparison, C is the winner, not B

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