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Voting

Voting. Part 1. Introduction. Mathematics plays an important role in the theory of voting. You can use mathematics to prove certain voting systems are “fair” or “unfair.” We’ll eventually look at some of these issues, but first we want to explore some different ways to count votes.

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Voting

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  1. Voting Part 1

  2. Introduction • Mathematics plays an important role in the theory of voting. • You can use mathematics to prove certain voting systems are “fair” or “unfair.” • We’ll eventually look at some of these issues, but first we want to explore some different ways to count votes. • For this purpose, we collect some data and try some voting methods. • But we’ll wait till later to see where the mathematics comes in.

  3. Which is your order of preference (from favorite to least favorite)? • [Coke, Pepsi, Dr. Pepper] • [Coke, Dr. Pepper, Pepsi] • [Pepsi, Coke, Dr. Pepper] • [Pepsi, Dr. Pepper, Coke] • [Dr. Pepper, Coke, Pepsi] • [Dr. Pepper, Pepsi, Coke]

  4. What is your order of preference for lunch (from favorite to least favorite)? • [McDonalds, Burger King, Wendy’s] • [McDonalds, Wendy’s, Burger King] • [Wendy’s, McDonalds, Burger King] • [Wendy’s, Burger King, McDonalds] • [Burger King, Wendy’s, McDonalds] • [Burger King, McDonalds, Wendy’s]

  5. What is your order of preference for favorite sport to watch? • [Football, Basketball, Baseball] • [Football, Baseball, Basketball] • [Baseball, Football, Basketball] • [Baseball, Basketball, Football] • [Basketball, Baseball, Football] • [Basketball, Football, Baseball]

  6. Majority Winner • If one of the choices receives more than 50% of the vote, then it is the majority winner. • If there are more than 2 choices (such as in our examples), then it’s possible that there is no majority winner.

  7. The majority winner is: • [Coke] • [Pepsi] • [Dr. Pepper] • [There is no majority winner]

  8. The majority winner is: • [McDonalds] • [Burger King] • [Wendy’s] • [There is no majority winner]

  9. The majority winner is: • [Football] • [Basketball] • [Baseball] • [There is no majority winner]

  10. Plurality Winner • The choice with the most first place votes is the plurality winner. • There always is at least one plurality winner. • The only way there could be more than one is if there is a tie.

  11. The plurality winner is: • [Coke] • [Pepsi] • [Dr. Pepper] • [There is no plurality winner]

  12. The plurality winner is • [McDonald’s] • [Wendy’s] • [Burger King] • [There is no plurality winner]

  13. The plurality winner is • [Football] • [Basketball] • [Baseball] • [There is no plurality winner]

  14. Condorcet Winner • One of the choices is a Condorcet winner if it defeats each of the other candidates in a head-to-head election. • For example, if there are 3 choices A,B,C, then look at your data, and cover up the occurrences of C. Is then A preferred more than B? Now cover up B, then A, and do the same test. Does one candidate defeat each of the others in head-to-head matchups? If so, it is the Condorcet winner. • It’s possible that an election does not have a Condorcet winner.

  15. The Condorcet Winner is: • [Coke] • [Pepsi] • [Dr. Pepper] • [There is no Condorcet Winner.]

  16. The Condorcet Winner is: • [McDonald’s] • [Wendy’s] • [Burger King] • [There is no Condorcet Winner.]

  17. The Condorcet Winner is: • [Football] • [Basketball] • [Baseball] • [There is no Condorcet Winner.]

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