2012 Best Picture 1. Votes st place A Z L 2nd place L L Z 3rd place Z A A
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1 2012 Best Picture 1 15 Academy Voters get together to compare their preferences for the 2012 Best Picture. The films under consideration are Argo, Life of Pi, and Zero Dark Thirty. Preference for the voters are summarized below Example (2012 Best Picture 1) Votes st place A Z L 2nd place L L Z 3rd place Z A A Which movie will win best picture if the Plurality method is What about if the Borda method is If the least favorite movie is removed from consideration, with all ballots reorganized (and preferences moved to fill missing gaps), which movie will win if Plurality is
2 Voting Method: Plurality with Elimination Definition (Method: Plurality with Elimination) Each voter casts a ballot for their favorite candidate. If one candidate receives a majority of first-place votes, then that candidate wins the election. If no candidate receives a majority of votes, then the candidate (or candidates) with the least number of votes is (are) eliminated, and a new election is held (with votes shifted from before). This continues until a single candidate receives a majority of 1st-place votes, and wins the election. Determining who gets 2nd place, 3rd place, etc... is more open using this method. We could make first elimination correspond to last place, 2nd elimination goes with 2nd to last place, etc..., but there are other ways as well. (Again, our main focus is usually only determining which candidate wins 1st place.)
3 2013 NCAA Football: Version 4 The purpose here is to practice, get some familiarity with Plurality with Elimination. Example (2013 NCAA Football 4) 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 st Place OSU OR LV AL OR 2nd Place AL AL OR LV LV 3rd Place OR LV AL OR AL 4th Place LV OSU OSU OSU OSU Using Plurality with Elimination, whichteamiseliminated first? Second? Which team wins using Plurality with Elimination?
4 One Direction Fan Club 2 Example (Lexington One Direction Fan Club 2) There are four choices for cutest band member (because no one likes Louis): Harry, Liam, Niall, and Zayn. Here s how the 40 person club votes: Votes st place H N Z N L 2nd place L H H L H 3rd place N L L Z Z 4th place Z Z N H N Using Plurality with Elimination, whichmemberiseliminated first? Second? Which member wins using Plurality with Elimination?
5 2012 Best Picture 2 15 Academy Voters get together to compare their preferences for the 2012 Best Picture. The films under consideration are Argo, Life of Pi, and Zero Dark Thirty. Preference for the voters are summarized below Example (2012 Best Picture 2) Votes st place A Z L 2nd place L L Z 3rd place Z A A If A is no longer a choice, which movie will win if Plurality is If L is no longer a choice, which movie will win if Plurality is If Z is no longer a choice, which movie will win if Plurality is
6 One Direction Fan Club 3.1 Example (Lexington One Direction Fan Club 3.1) There are four choices for cutest band member (because no one likes Louis): Harry, Liam, Niall, and Zayn. Here s how the 40 person club votes: Votes st place H N Z N L 2nd place L H H L H 3rd place N L L Z Z 4th place Z Z N H N If L and Z are no longer choices, who will win if Plurality is If N and Z are no longer choices, who will win if Plurality is
7 One Direction Fan Club 3.2 Example (Lexington One Direction Fan Club 3.2) There are four choices for cutest band member (because no one likes Louis): Harry, Liam, Niall, and Zayn. Here s how the 40 person club votes: Votes st place H N Z N L 2nd place L H H L H 3rd place N L L Z Z 4th place Z Z N H N If H and L are no longer choices, who will win if Plurality is If H and Z are no longer choices, who will win if Plurality is
8 One Direction Fan Club 3.3 Example (Lexington One Direction Fan Club 3.3) There are four choices for cutest band member (because no one likes Louis): Harry, Liam, Niall, and Zayn. Here s how the 40 person club votes: Votes st place H N Z N L 2nd place L H H L H 3rd place N L L Z Z 4th place Z Z N H N If H and N are no longer choices, who will win if Plurality is If L and N are no longer choices, who will win if Plurality is
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