There are many situations in which there is a need to know not only the winner of the el...

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.

An extension of the plurality method can be used to rank candidates according to the number of first place votes received. How would the candidates from problem 4 be ranked using this extension of the plurality method?

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?