Refer to the preference table from problem 38. a. Suppose that the plurality with elim...

Refer to the preference table from problem 38.

a. Suppose that the plurality with elimination method is modified by using the following runoff elections. The first runoff election is between the two candidates with the lowest number of first-place votes; the second uses the winner of the runoff contest and the candidate with the second-highest number of first-place votes; and finally, the third uses the winner of the second runoff contest and the candidate with the most original first-place votes. If the number of first-place votes is a tie, the order is determined by the number of second-place votes. Who is selected as team captain if this method is implemented?

b. Who would be selected if plurality with elimination is used and the two candidates with the most first-place votes are matched in a runoff election?

Problem 38:

Four seniors on the baseball team, Joe Aaron (A), Billy Bonds (B), Mike Griffey (G), and Tim Ruth (R), are being considered for team captain. The 21 other members of the team are asked to rank them in order of preference from first to fourth. The ballots are grouped as follows.

a. Who is selected as team captain using the plurality method?

b. Who is selected as team captain using the plurality method with elimination?

c. Who is selected as team captain using the Borda count method?

d. Who is selected as team captain using a modified Borda count method with assigned values of 6 points for first place, 3 points for second, 2 points for third, and 1 point for fourth?