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Plurality-with-Elimination Method (Instant Runoff Voting)

Plurality-with-Elimination Method (Instant Runoff Voting). Notes 3 – Section 1.4. Essential Learnings. Students will understand and be able to use the Plurality-with-Elimination Method to determine the winner of an election. Plurality-with-Elimination Method.

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Plurality-with-Elimination Method (Instant Runoff Voting)

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  1. Plurality-with-Elimination Method(Instant Runoff Voting) Notes 3 – Section 1.4

  2. Essential Learnings • Students will understand and be able to use the Plurality-with-Elimination Method to determine the winner of an election.

  3. Plurality-with-Elimination Method • When there are three or more candidates running in an election, it is often the case that no candidate gets a majority. • Typically, the candidate with the fewest first-place votes is eliminated and a runoff election is held (EXPENSIVE). • Using preference ballots allows voters to rank their choices making a runoff election unnecessary.

  4. Plurality-with-Elimination Method • Round 1: Count the first-place votes for each candidate. If a candidate has a majority of first-place votes, then that candidate is the winner. Otherwise, eliminate the candidate (or candidates if there is a tie) with the fewest first-place votes.

  5. Plurality-with-Elimination Method • Round 2: Cross out the name(s) of the candidates eliminated from the preference schedule and recount the first-place votes. If a candidate has a majority of first-place votes, then declare that candidate the winner. Otherwise, eliminate the candidate with the fewest first-place votes.

  6. Plurality-with-Elimination Method • Round 3, 4 . . . . Repeat the process, each time eliminating one or more candidates until there is a candidate with a majority of first-place votes. That candidate is the winner of the election.

  7. Math Club Election • Determine the winner using the Plurality-with Elimination Method.

  8. Math Club Election • Winner: D (Dave) • The Plurality Method – Alisha was winner • The Borda Count Method – Boris was the winner • Interesting…

  9. Electing the Mayor of Kingsburg • Determine the winner using the Plurality-with Elimination Method.

  10. There Go the Olympics • Three cities competing to host Summer Olympics: A – Athens, B – Barcelona, C – Calgary • Decision made by secret vote of 29 members of Executive Council of the IOC. • Two days prior to election, a straw poll is held.

  11. There Go the Olympics • Preference schedule for straw poll: • Since C looks like it will win, the voters in the last column decide to switch their first and second votes. It won’t change anything right?

  12. There Go the Olympics • Preference schedule for official election: • Determine the winner.

  13. The Monotonicity Criterion • If candidate X is a winner of an election and, in a reelection, the onlychanges in the ballots are changes that favor X (and only X), then Xshould remain a winner of the election. • The Plurality-with-Elimination Method violates the monotonicity criterion and the Condorcet criterion.

  14. Assignment p. 33: 27 a-c, 28, 30, 31, 34 Quiz Tomorrow (sections 1.1-1.4) Covered Textbooks

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