Voting Lecture 5: Bracket Voting Spring Morgan Schreffler Office: POT Teaching.php
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1 Voting Lecture 5: Bracket Voting Spring 2014 Morgan Schreffler Office: POT Teaching.php
2 NCAA Basketball Example (NCAA Basketball) 6 coaches give informal rankings to 4 college basketball teams. Their predictions for Indiana (I), Louisville (L), Ohio State University (O), and Kentucky (K) are given below: Number of Votes st place K L I O 2nd place L O K L 3rd place O I O I 4th place I K L K Which team(s) will Kentucky beat if the Pairwise Comparison method is used? Which team(s) will Kentucky lose to if the Pairwise Comparison method is used?
3 NCAA Basketball Example (NCAA Basketball 2) Use the voting information for the previous question to fill in a bracket where Kentucky is the winner of the bracket. K
4 Voting Method: Bracket Voting Definition (Method: Bracket Voting) Each voter gives a complete ranking of the candidates. Using the voter rankings, make a Matchup Chart (as you would if you were using the Pairwise Comparison method). A predetermined candidate (you are always told which one) is chosen to be the winner. Cross Out all matchups where that candidate loses. If the candidate loses ALL matchups then the candidate cannot win under Bracket Voting. Start by arranging the candidates in a Bracket so that the chosen candidate beats another candidate. Then use the comparisons to find a third candidate that either of the first two candidates can beat. Repeat this process until all candidates appear in the bracket. The shape of the bracket may vary with examples and choices made.
5 New Breaking Bad Fan Club Example (A New Breaking Bad Fan Club) The Lexington Breaking Bad fan club adds two members (now a total of 42). As before, the four choices for favorite male character are: Hank, Jesse, Saul, and Walt. Here s how the 42 person club votes: Votes st place H W S W J 2nd place J H H J H 3rd place W J J S S 4th place S S W H W Who does Saul beat under the Pairwise Comparison method? Who beats Saul under the Pairwise Comparison method?
6 New Breaking Bad Fan Club Example (A New Breaking Bad Fan Club) The Lexington Breaking Bad fan club adds two members (now a total of 42). As before, the four choices for favorite male character are: Hank, Jesse, Saul, and Walt. Here s how the 42 person club votes: Votes st place H W S W J 2nd place J H H J H 3rd place W J J S S 4th place S S W H W Who can Saul beat using the Pairwise Comparison method? Who can that person beat? Design a bracket (with a different shape) where Saul will win.
7 New Breaking Bad Fan Club Example (A New Breaking Bad Fan Club) The Lexington Breaking Bad fan club adds two members (now a total of 42). As before, the four choices for favorite male character are: Hank, Jesse, Saul, and Walt. Here s how the 42 person club votes: Votes st place H W S W J 2nd place J H H J H 3rd place W J J S S 4th place S S W H W Who can Walt beat using the Pairwise Comparison method? Who can that person beat? Design a bracket that will guarantee Walt will win.
8 Lamest Gus-themed Star-Wars Title Example (Lamest Gus-themed Star-Wars Title) Before class, a poll was taken to decide which of the previous Star Wars-themed examples was the lamest. The candidates are The Canine Menace (CM), Revenge of the Shih-Tzu (RS) and A Chew Hope (CH). The following preferences were recorded: Votes st place CM CH CH RS 2nd place CH RS CM CM 3rd place RS CM RS CH Design a bracket so that Revenge of the Shih-Tzu (RS) wins? What way can you increase the blue votes so that Revenge of the Shih-Tzu (RS) wins under ANY bracket?
9 School Board Election Example (School Board Election) Below is a summary of the previous School Board Election. The winner of Head-to-Head Comparisons are given: Comp. Winner Comp. Winner Comp. Winner A vs B A B vs C C C vs D C A vs C A B vs D B A vs D D Can you make a bracket where Candidate B is the winner? If Candidate D drops out, can you make a bracket where Candidate B is the winner? What does this say about the bracket voting system and fairness?
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