The student body at Eisenhower High School is having an election for Homecoming
ID: 2902488 • Letter: T
Question
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.
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
Explanation / Answer
a. Students voted = 143+110+43+241+53+31+110+152+183+142 = 1208.
b. Since there are a total of 1208 votes, a candidate must get at least 605 votes (more than half) to have a majority.
c. Lets calculate the first choice votes for each candidate:
A: 143+110+43=296
B: 241+53+31=325
C:110+152=262
D: 183+142=325
We can see here that there is a tie between candidate B and candidate D.
so now we go for the tie breaking rule.
d. Last place votes for B: 43+110+183=336
for D: 143+31+152=326
so fewest votes is D and hence he is chosen as the king.
e. total votes forB and total votes for D recieved.
f.
The Borda Count Method
For the Borda Count Method, each candidate (or alternative) gets 1 point for each last place vote received, 2 points for each next-to-last point vote, etc., all the way up to N points for each first place vote (where N is the number of candidates/alternatives). The candidate with the largest point total wins the election.
Notice that the Plurality Method uses only the first row of information in the preference schedule (corresponding to first place votes). When using the Plurality method, all of the other information in the preference schedule is irrelevant.
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