The following questions review the main ideas of this chapter. Write your answers to the...

The following questions review the main ideas of this chapter. Write your answers to the questions and then refer to the pages listed by number to make certain that you have mastered these ideas.

How are rankings used to select a winner using the pairwise comparison method? pgs. 149–150

Reference:

We have so far considered how two different voting methods use voters’ rankings to select a winning candidate: the Borda count method and the plurality with elimination method. Another way of choosing between more than two alternatives, called the pairwise comparison method uses rankings to compare pairs of candidates. When the pairwise comparison method is used, each voter must make a choice between every possible pair of candidates. For example, if the candidates are Franklin, Goldstein, and Hernandez, we could ask the voters to vote three times in contests of Franklin versus Goldstein, then Franklin versus Hernandez, and finally Goldstein versus Hernandez. However, instead of asking voters to complete three separate ballots, we will require the voters to rank the candidates. So if one particular voter ranks the three candidates as

Hernandez

Goldstein

Franklin,

we will assume this voter would vote for Hernandez over Goldstein in the Goldsteinversus-Hernandez contest, for Hernandez over Franklin in the Franklin-versus-Hernandez contest, and for Goldstein over Franklin in the Franklin-versus-Goldstein contest.

Using the rankings, we go through every possible pairing of candidates and determine which of the two is preferred based on the rankings. Candidates will be assigned points based on how well they do with respect to the other candidates. In each contest, one point is awarded to the candidate preferred by the greatest number of voters, and 1/2 point is awarded to each candidate if the two candidates are preferred by the same number of voters.