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.

What is an advantage of the Borda count method over the plurality method? pg. 145 What is a disadvantage of the plurality with elimination method? pgs. 146–147

Reference:

Another means of selecting a winner from a group of candidates involves reducing the size of the candidate pool until one candidate receives more than half the votes. When the plurality with elimination method is used for choosing among several candidates, a series of votes may be required. In the first round:

• Each voter votes for his or her preferred candidate.

• If one candidate wins a majority of votes, then that candidate is selected.

• If no candidate attains a majority, then the candidate receiving the fewest votes is eliminated.

If there are ties for this distinction, all candidates with the fewest votes are dropped.

Another round of voting is performed under the same rules, so again, either one candidate attains a majority or at least one candidate is eliminated. Eventually a decision is reached.

If no candidate receives a majority and if, because of a tie, eliminating the candidates with the fewest votes leaves only one candidate, then a tie-breaking procedure must be used to ensure that there will be at least two candidates in the next round of voting. We will avoid this sort of example here, but it can happen.

Plurality with elimination methods sometimes use other rules to decide which candidates are in the second (or later) round of voting. For example, the top two candidates may be the only candidates left for the second round. (If only two candidates are left for the second round of voting, then the second round is often called a runoff election.) Including all its variations, the plurality with elimination method is probably the most widely used voting method. For example, this method is used to determine the site for the Olympic Games every two years, and the President of France is now chosen using a plurality with elimination method. However, the 2002 presidential elections in France highlighted a common problem with the method of plurality with elimination. Under the French system, citizens typically vote twice. In the first round, the election is over if a majority is achieved by one candidate. If a majority has not been reached, then a runoff election is held, in which citizens vote again to choose between the top two candidates. In the first round of voting, held on Sunday, April 21, 2002, none of the 16 presidential candidates received a majority. The top two candidates were Jacques Chirac, who received 19.9% of the vote, and Jean-Marie Le Pen, with 16.9% of the vote. A close third, Lionel Jospin, received 16.2% of the vote. Notice that the top two candidates won only 36.8% of the vote. Almost two-thirds of voters favored the other candidates. In the May 5 runoff election between the top two candidates, Chirac defeated LePen 82.2% to 17.8%. This situation, in which the winning candidate clearly did not have majority support, led to calls for reform in France’s electoral system. In particular, it lent support to the idea of letting voters rank their preferences for president rather than simply voting for one candidate. In the French system, two rounds of voting are required. In general, however, many rounds of voting may be required to carry out the plurality with elimination method we described because our rules eliminate only one candidate after each round of voting. To consider what happens in successive rounds of voting, we will assume that each voter has ranked all the candidates, as in the Borda count method. In each round of voting, the voters cast their votes for the highest-ranking candidates still being considered. For example, suppose that before the first election one voter ranked Garcia, Johnson, and Smith first, second, and third, respectively, so that her ballot read as follows:

Garcia

Johnson

Smith

If Garcia was eliminated after the first round of voting, then we will assume that this particular voter would vote for Johnson (her highest-ranking remaining candidate) in the second round of voting. This is a simplifying assumption, since real voters do not always behave in such a predictable way. In the next example, we assume that voters have ranked all the candidates, and these rankings are displayed in what we call a preference table. In the first round, voters cast their votes for their first-choice candidate. If a candidate must be eliminated because no candidate received a majority of votes, the first-place votes of the eliminated candidate go instead to the second-place choices of those voters who ranked him or her first. This action simulates running another ballot. In an actual election, voters may dislike ranking all the candidates because this forces them to make choices that may turn out to be unnecessary. However, ranking the candidates in the first place may allow citizens to avoid having to vote a second time.