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 with elimination method is explained in the previous problem. Use this extension to rank the cities from problem 20.

Problem 20:

The board of directors of a large company is choosing a site for a new branch office in the southwest. The cities being considered are Albuquerque (A), Phoenix (P), Sante Fe (S), and Tucson (T). The members of the board are asked to rank the cities from first to fourth. The results are summarized in the following preference table. Although there are 24 ways to rank the cities, only those shown in the table are used.

a. Which city is chosen using the plurality with elimination method?

b. Which city is selected if the pairwise comparison method is used?