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Voting systems

Voting systems. Plurality voting. Plurality voting refers to elections in which more than one candidate is to be chosen There are multiple reasons One reason: so that everyone gets a chance to have their view represented Second reason: so that the right combination of candidates gets chosen.

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Voting systems

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  1. Voting systems

  2. Plurality voting • Plurality voting refers to elections in which more than one candidate is to be chosen • There are multiple reasons • One reason: so that everyone gets a chance to have their view represented • Second reason: so that the right combination of candidates gets chosen

  3. Plurality voting system • Plurality voting is used in 43 of the 191 countries in the United Nations for either local or national elections. • In single winner plurality voting, each voter is allowed to vote for only one candidate, and the winner of the election is whichever candidate represents a plurality of voters, that is, whoever received the largest number of votes. • it is however very contentious to draw district boundary lines in this system • Plurality voting is based on minimal information

  4. Example: class president election (compare to Bush, Gore, Nader) • Suppose: Each class has a president, who sits on a school council. Further assume that, in this imaginary school, male and female students disagree on many issues; students prefer to vote for candidates of their gender. • Three candidates: Tofu, Milo and Leila. Each class member gets a ballot, with these three names on it. Each voter must put an "X" by one of the names on their ballot. • Votes for Tofu, for Milo, and for Leila placed in separate piles.

  5. Milo Wins • with only 40% of the vote • Electors only vote once

  6. Plurality voting • Suppose that candidates are ranked (1-3). Then Milo might be the favorite of fewer than half the voters. • In some systems a runoff election among the top placing voters is called for.

  7. advantages/disadvantages • OMOV • Constituency • Tactical voting • Party effects (block voting) • Wasted votes (< majority) • Manipulation

  8. Multiple step voting • Runoffs • Diminish tactical voting • Majority rule (if enough steps) • Voter burnout

  9. Single transferable vote: a compromise • Here’s an example: • The student council wants to organize a rock concert • A list of 5 bands is considered as candidates but the council can only afford 3 bands. There are twenty council members who list their preferences

  10. Only first two preferences shown

  11. Setting the quota • Droop quota • (votes/(seats+1))+1 =20/4+1=6

  12. Finding the winners • Any candidate who has reached or exceeded the required quota is declared elected • If not enough candidates have been elected, the count continues. • If a candidate has more votes than the quota, then their surplus is transferred proportionally with rounding to remaining candidates according to the next preference on each voter's ballot. • If no one meets the quota, the candidate with the fewest votes is eliminated and their votes are transferred. • Repeat from first step until the seats are filled

  13. Round 1 • Fiery furnaces meet the quota. They are chosen

  14. Round 2 • Furnace excess transferred to Best Coast and Matmos based on second choices. No quota. Dum Dum Girls eliminated

  15. Round 3 • Dum Dum Girls votes transferred to second choice. St Vincent reaches quota; no extra votes

  16. Round 4 • No remaining candidate meets quota. Matmos eliminated

  17. Call for nominations • I’m going to conduct a popularity poll • I need six (6) nominations for “Favorite Bands of Math 210” • Prior winners of TV show contests not allowed • The “Pride” not allowed. • Someone else in the class has to have heard of the band • Your homework: figure out the “top 3” bands based on the STV method

  18. Clicker ballot. Note: your clicker must be in numerical mode. • Rank order bands • 1= • 2= • 3= • 4= • 5= • 6= • In your order of preference

  19. Recap • Mathematics: seeks optimal solution • Voting: optimally represent public opinion • No voting system is perfect • Outcome often depends on system employed

  20. Lattice models for “opinion” • Renormalization in physics • Ising/Potts model applet: renormalization group algorithm

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