The members of Student Council decide to vote on the type of music to play at an upcoming school dance. Their schedule of preference is as follows:
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| First Choice | Jazz | Rock | Country | New Wave | Oldies | Oldies |
| Second Choice | New Wave | Oldies | Rock | Country | Rock | Country |
| Third Choice | Oldies | New Wave | Oldies | Oldies | New Wave | New Wave |
| Fourth Choice | Country | Country | New Wave | Rock | Country | Rock |
| Fifth Choice | Rock | Jazz | Jazz | Jazz | Jazz | Jazz |
a. Which type of music wins if they use the plurality method?
b. Which one wins if they use a Borda count that assigns 5,4,3,2, and 1 points to each first, second, and third choice, respectively? Could the number of points assigned to each place be modified to change the winner?
c. Which one wins if they decide to hold a runoff election between the top two contenders?
d. Which one wins if they first eliminate the one with the most last-place votes and have a sequential runoff with the others?
e. What verdict would result if they used the Condorcet method? Assume the students vote sincerely.