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.

Extend the pairwise comparison method, explained in the previous problem, to rank the candidates from problem 25.

Problem 25:

The following table contains preferences of faculty members for students being considered for scholarships. The first-place candidate will receive a $5000 scholarship while second-, third-, and fourth-place candidates will receive $4000, $3000, and $2000, respectively. Rank the candidates in order according to their Borda count totals and determine which candidate receives which scholarship.