Chapter 4.2, Problem 41ES

Another method of voting is to assign a ‘weight.” or score, to each candidate rather than ranking the candidates in order. All candidates must receive a score, and two or more candidates can receive the same score from a voter. A score of 5 represents the strongest endorsement of a candidate. The scores range down to 1, which corresponds to complete disapproval of a candidate. A score of 3 represents indifference. The candidate with the most total points wins the election. The results of a sample election are given in the table.

a. Find the winner of the election.

b. If plurality were used (assuming that a person’s vote would go to the candidate that he or she gave the highest score to), verify that a different winner would result.