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Exploring Different Voting Methods: Preferences and Winners

This introduction delves into voting theory using mathematics to evaluate fairness of systems. Discover various vote counting methods and determine majority, plurality, and Condorcet winners.

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Exploring Different Voting Methods: Preferences and Winners

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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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