Question Description

For this module’s assignment review the following.

A group of students were asked to vote on their favorite horror films. The candidate films are: Abraham Lincoln Vampire Hunter, The Babadook, Cabin Fever, and Dead Snow (A, B, C, D for short). The following table gives the preference schedule for the election.

Number of voters 10 7 5 5 4
1st choice A D B C B
2nd choice C B C D C
3rd choice B A A A D
4th choice D C D B A
  1. How many students voted? How many first place votes are needed for a majority?
  2. Use the plurality method to find the winner of the election.
  3. Use the Borda count method to find the winner of the election.
  4. Use the plurality-with-elimination method to find the winner of the election.
  5. Use the pairwise-comparisons method to find the winner of the election.
  6. Three players (April, Brandy and Cindy) are sharing a cake. Suppose that the cake 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. (A fair share would be 1/3 = 0.333 = 33.3% or greater.)
    s1 s2 s3
    April $4.50 $5.50 $5.00
    Brandy $5.50 $5.25 $5.00
    Cindy $5.60 $5.00 $5.00
    1. Which of the three slices are fair shares to April?
    2. Which of the three slices are fair shares to Brandy?
    3. Which of the three slices are fair shares to Cindy?
    4. Find a fair division of cake using S1, S2, and S3 as fair shares. If this is not possible, explain why not.
  7. Three players (Adam, Bob and Chad) 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. (A fair share would be 1/3 = 0.333 = 33.3% or greater.)
    s1 s2 s3
    Adam 30% 50% 20%
    Bob 32% 36% 32%
    Chad 30% 35% 35%
    1. Which of the three slices are fair shares to Adam?
    2. Which of the three slices are fair shares to Bob?
    3. Which of the three slices are fair shares to Chad?
    4. 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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