Refer to the preference table in problem 38. a. Suppose that the plurality with elimin...

Refer to the preference table in problem 38.

a. Suppose that the plurality with elimination method is modified as follows. First, a runoff election takes place between the candidates who rank second and third in terms of first-place votes; then, the winner of the runoff is matched against the candidate who originally had the most first-place votes. Who is selected as team captain if this method is implemented?

b. Who would be selected as baseball team captain if the plurality with elimination method is used, and the candidate with the most last-place votes is eliminated at each step? This method eliminates candidates who are least preferred.

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?