The student body at Eisenhower High School is having an election for Homecoming King. The candidates are Aaron, Brad, Charles and David (A, B, C, D for short). The following table gives the preference schedule for the election.
|
Number of votes
|
143
|
110
|
43
|
241
|
53
|
31
|
110
|
152
|
183
|
142
|
|
|
1st choice
|
A
|
A
|
A
|
B
|
B
|
B
|
C
|
C
|
D
|
D
|
|
|
2nd choice
|
C
|
B
|
D
|
D
|
C
|
C
|
A
|
B
|
A
|
B
|
|
|
3rd choice
|
B
|
D
|
C
|
A
|
D
|
A
|
D
|
A
|
C
|
C
|
|
|
4th choice
|
D
|
C
|
B
|
C
|
A
|
D
|
B
|
D
|
B
|
A
|
|
a. How many students voted?
b. How many first place votes are needed for a majority?
c. Use the plurality method to find the winners of the election.
d. Tie-breaking rule: If there more than one alternative with a plurality of the first-place votes, then the tie is broken by choosing the alternative with the fewest last-place votes. Who would be the Homecoming King under this tie-breaking rule?
e. A different tie-breaking rule: If there are two candidates tied with plurality of the first-place votes, the tie is broken by head-to-head comparison between the two candidates. Who would be the Homecoming King under this tie-breaking rule?
f. Using the Borda Count Method, find the winner of the election.
g. Use the plurality-with-elimination method to find the winner of the election.