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 16, and who would be elected mayor of Tinytown, if 4 points are given for first-place votes, 2 for second place, and 1 for third place?

Problem 16:

Three candidates, Able, Boastful, and Charming are running for the office of mayor of Tinytown. 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 wins using the Borda count method?

b. Who wins using the plurality method?