G180 Module 05 Assignment
For Halloween, a group of students were asked to vote for their favorite horror movies. Their choices were Alien, The Blair Witch Project, The Conjuring, and Dreamcatcher (A, B, C, D for short). The following table gives the preference schedule for the election.
| Number of Voters | 17 | 14 | 12 | 8 | 7 |
| 1st Choice | C | A | B | D | B |
| 2nd Choice | D | B | D | A | D |
| 3rd Choice | B | C | C | C | A |
| 4th Choice | A | D | A | B | C |
- Use the pairwise-comparisons method to find the winner of the election.
- Three players (Anna, Bill and Carol) are sharing a pizza. Suppose that the pizza is divided into three slices (s1, s2, s3). The following table gives the value of each slice in the eyes of each of the players.
Assumption, share fair 1/3 or greater
| s1 | s2 | s3 | |
| Anna | $5.50 | $5.25 | $5.00 |
| Bill | $4.50 | $5.50 | $5.00 |
| Carol | $5.60 | $4.60 | $5.00 |
- Which of the three slices are fair shares to Anna?
- Which of the three slices are fair shares to Bill?
- Which of the three slices are fair shares to Carol?
- Find a fair division of pizza using S1, S2, and S3 as fair shares. If this is not possible, explain why not.
- Three players (April, Beth and Clint) are sharing a cake. Suppose that the cake is divided into three slices (s1, s2, s3). The percentages represent the value of the slice as a percent of the value of the entire cake.
Assumption, share fair 1/3 or greater
| s1 | s2 | s3 | |
| April | 30% | 35% | 35% |
| Beth | 36% | 32% | 32% |
| Clint | 30% | 42% | 28% |
- Which of the three slices are fair shares to April?
- Which of the three slices are fair shares to Beth?
- Which of the three slices are fair shares to Clint?
- Find the fair division of the cake, using s1, s2 and s3 as fair shares. If this is not possible, explain why not.
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