Voting Terminology: Ballot
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1 Voting Terminology: Definition () A ballot is a ranked list of all the options (candidates) a person can vote for in an election. Steve is voting in an election for class president. The students running for president are Albert, Brenda, Chris, and Dave. Steve s ballot looks like 4th Brenda Dave Chris Albert This means that Steve thinks Brenda is the best choice, Dave is the second-best choice, Chris is the third-best choice, and Albert is the worst choice for president.
2 Voting Terminology: Preference Schedule It is often convenient to combine many ballots into a preference schedule to make it easier to put a lot of information into a small space. Definition (Preference Schedule) A preference schedule is a table which lists the results of many ballots cast for the same election in compact form. Each student in Steve s grade votes for class president. The results are summarized in the following preference schedule. Votes A B C B D D C C B 4th D A A
3 Where do we eat? Example (Where do we eat?) Four friends are trying to decide where they should eat. They RANK their preferences with the following results: Burgers Pizza Mexican Burgers Pizza Mexican Pizza Mexican Burgers Mexican Pizza Burgers Given the above preferences, where should they eat? Give a reason that supports a di erent restaurant choice than the one you gave above.
4 Voting Method: Plurality Definition (The Plurality Method of Voting) For each ballot, only the first place vote counted. The candidate with the most first place votes is the winner. If ballots are combined into a preference schedule then the Plurality method will ignore all non- place votes. We could also determine who gets place, place, etc... ranking the candidates based on their -place votes (However, our main focus is usually only determining which candidate wins place.) Definition A candidate in an election is a Majority Candidate if they receive over 50% of -place votes.
5 Best Bad Movie 1 Example (Best Bad Movie 1) Stuart Wellington of the Flophouse podcast asks two of his friends to rate the best bad movie. The candidates are Castle Freak (CF), Invisible Maniac (IM) andhead of the Family (HF). He and his friends give the following preferences: CF IM HF IM CF HF HF CF IM Which movie will win if the Plurality method is used? Which movie do you think should win?
6 What to eat?: Version 1 Example (What to eat? Version 1) (From In Defense of Food by Michael Pollan) A group of Americans were asked the following: Assume you are alone on a desert island for one year and can have water and one other food. Pick the food you think would be best for your health. The choices are Alfalfa sprouts, Bananas, Corn, Hot Dogs, Milk Chocolate, Peaches, or Spinach. % Votes Place A B C H M P S Which food wins if the Plurality method is used? Which food do you think would be best for your health?
7 What to eat?: Version 2 Example (What to eat? Version 2) (From In Defense of Food by Michael Pollen) Assume you are alone on a desert island for one year and can have water and one other food. Pick the food you think would be best for your health. The choices are Alfalfa sprouts, Bananas, Corn, Hot Dogs, Milk Chocolate, Peaches, or Spinach. % Votes Place A B C H M P S Place S C S C C S P If people are told to include place choices as well, what ONE food do you think should be chosen? If people are told to include place choices as well, what TWO foods do you think should be chosen?
8 2013 NCAA Football: Version 1 Example (2013 NCAA Football 1) 37 Sports Writers made predictions for the top 4 rankings in 2013 NCAA football. Their predictions for Alabama (AL), Louisville (LV), Ohio State University (OSU), and Oregon (OR) are given below: Number of Votes Place OSU OR LV AL OR Place AL AL OR LV LV Place OR LV AL OR AL 4th Place LV OSU OSU OSU OSU Which school wins if the Plurality method is used to select the winner? Give a reason that supports a di erent team choice than the answer above.
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