The student body at Eisenhower High School is having the election for Homecoming King. Candidates are Aaron, Brad, Charles and David (A, B, C, D for short). The given table provides preference schedule for 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
|
|
i) How many students voted?
ii) How many first place votes are required for the majority?
iii) Use plurality method to determine winners of election.
iv) Tie-breaking rule: If there more than one alternative with the plurality of first-place votes, then tie is broken by selecting alternative with fewest last-place votes. Who would be Homecoming King under tie-breaking rule?
v) The different tie-breaking rule: If there are 2 candidates tied with plurality of first-place votes, tie is broken by head-to-head comparison between two candidates. Who would be Homecoming King under tie-breaking rule?
vi) Using Borda Count Method, compute winner of the election.
vii) Use plurality-with-elimination method to determine winner of election.