A modified Borda count method is used in many types of contests other than elections, su...

A modified Borda count method is used in many types of contests other than elections, such as athletic events. A fairly common practice is to emphasize first-place finishes, or to de-emphasize other finishes, by changing the way in which points are awarded (such as 5 points for first place, 3 for second place, 2 for third place, and 1 for fourth place).

How many points would each candidate receive in problem 15, and who would be elected senior class president, if 4 points are given for first-place votes, 2 for second place, and 1 for third place?

Problem 15:

There are three candidates running for president of the senior class: Peter, Carmen, and Shawna. Voters mark their ballots to indicate their first, second, and third choices (only ballots with all three choices marked are valid). The results are summarized as follows:

a. Who is elected president using the Borda count method?

b. Who is elected president using the plurality method?