37-41: Preference Schedules. Consider the following preference schedules:

a. How many votes were cast?

b. Find the plurality winner. Did the plurality winner also receive a majority? Explain.

c. Find the winner of a runoff between the top two candidates.

d. Find the winner of a sequential runoff.

e. Find the winner by a Board count.

f. Find the winner if any by the method of pairwise comparisons.

g. Summarize the results of the various methods of determining a winner. Based on these results, is there a clear winner? If so, why? If not, which candidate should be selected as the winner, and why?

The answers for 37 are:

a. A total of 66 votes were cast.

b. Is the plurality winner (but not by a majority).

c. D is the winner of the top-two runoff.

d. The winner of a sequential runoff is D.

e. D is the winner by the Board count.

f. D wins by the meth of pairwise comparisons.

g. As the winner by all five methods Candidate D is clearly the winner of the election.

37. First Second D OUDO Third A Fourth B Number of voters 20 15 10 8 7