There are many situations in which there is a need to know not only the winner of the election, but also how the other candidates ranked. Each of the methods we have studied can be extended to produce a winner and rank the other candidates for second place, third place, etc.
The members of the football team will select a senior captain and a junior captain from three candidates. Use the preference table from problem 4 and extend the Borda count method to rank the candidates according to their Borda count totals. The first-place candidate will be the senior captain, and the second-place candidate will be the junior captain. What are the results of the election?
Problem 4:
The members of the football team selected their team captain from three of the seniors: Jorgensen, Petrini, and Ramirez. Each player ranked his choices from first to third, and 88 players completed ballots. There are six ways to rank the choices; the following table shows the number of players who ranked the candidates in a given order.
a. How many first-place votes would be required for a majority win?
b. How many first-place votes did each person receive?
c. Under the plurality method, who is selected as team captain?
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