# voting theory amp game theory i 1

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 |

1 |
A |
D |
B |
C |
B |

2 |
C |
B |
C |
D |
C |

3 |
B |
A |
A |
A |
D |

4 |
D |
C |
D |
B |
A |

- How many students voted? How many first place votes are needed for a majority?
- Use the plurality method to find the winner of the election.
- Use the Borda count method to find the winner of the election.
- Use the plurality-with-elimination method to find the winner of the election.
- Use the pairwise-comparisons method to find the winner of the election.
- Three players (April, Brandy and Cindy) are sharing a cake. Suppose that the cake is divided into three slices (s
_{1}, s_{2}, s_{3}). 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.)

s _{1}s _{2}s _{3}April $4.50 $5.50 $5.00 Brandy $5.50 $5.25 $5.00 Cindy $5.60 $5.00 $5.00 - Which of the three slices are fair shares to April?
- Which of the three slices are fair shares to Brandy?
- Which of the three slices are fair shares to Cindy?
- Find a fair division of cake using S
_{1}, S_{2}, and S_{3}as fair shares. If this is not possible, explain why not.

- Three players (Adam, Bob and Chad) are sharing a cake. Suppose that the cake is divided into three slices (s
_{1}, s_{2}, s_{3}). 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.)

s _{1}s _{2}s _{3}Adam 30% 50% 20% Bob 32% 36% 32% Chad 30% 35% 35% - Which of the three slices are fair shares to Adam?
- Which of the three slices are fair shares to Bob?
- Which of the three slices are fair shares to Chad?
- Find the fair division of the cake, using s
_{1}, s_{2}and s_{3}as fair shares. If this is not possible, explain why not.

PLEASE USE THE ATTACHED WORKSHEET TO FILL OUT ANSWERS!