Dance Music

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:
Number of Students
18
12
10
9
4
2
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.


The Discrete Mathematics Project