14.2 Flaws of the Voting Methods 915 Of the four methods we discussed, only the Borda count method can violate the majority criterion. Therefore, the Borda count method has a flaw that none of the other voting methods has. An advantage of the Borda count method is that it takes into account voters’ preferences by having all candidates ranked. However, a candidate with a majority of first-place votes can lose an election with the Borda count method. Next we will introduce a second fairness criterion and use it to uncover flaws in other voting methods. Head-to-Head Criterion Suppose that it is determined that one candidate is preferred over each of the other candidates using head-to-head comparisons. It would seem reasonable that this candidate should be chosen as the winner. That, however, is not always the case, and the head-to-head criterion will be used to uncover the next voting method flaw. Example 2 Applying the Majority Criterion International Beverage Group is deciding which variety of kombucha A, B, or C to involve in an ad campaign. Preference Table 14.16 shows the 33 board of directors members’ preferences. Decide which candidate would be chosen with each of the following voting methods. Also discuss whether or not the method violates the majority criterion. a) The plurality method b) The Borda count method c) The plurality with elimination method d) The pairwise comparison method Solution a) The plurality method awards the election to A. Notice that A also has a majority, 17 out of 33, of first-place votes. The plurality method does not violate the majority criterion. In general, a candidate who holds a majority of first-place votes also holds a plurality of first-place votes. Therefore, the plurality method never violates the majority criterion. However, that does not mean that the plurality method always produces a winner that has a majority of the votes. It does mean that if a candidate has a majority of first-place votes, that candidate will also have a plurality of votes and will be selected with the plurality method. b) The Borda count method awards the election to candidate B. Since candidate A holds a majority of first-place votes, this method violates the majority criterion. This example is the second example in which the Borda count method violates the majority criterion. The Borda count method does not always violate the majority criterion; however, from our examples, we can conclude that the Borda count method has the potential for violating the majority criterion. c) The plurality with elimination method awards the election to candidate A. Therefore, the majority criterion is not violated. In general, a candidate who holds a majority of first-place votes is awarded the election without having to hold a second election, or without having to consider eliminating a candidate and then realigning voters’ choices. Therefore, the plurality with elimination method never violates the majority criterion. d) The pairwise comparison method awards the election to candidate A. In general, if a candidate holds a majority of first-place votes, this candidate always wins every pairwise comparison, thereby granting this candidate the victory. Thus, the pairwise comparison method never violates the majority criterion. 7 Now try Exercise 29 Table 14.16 Kombucha Preference Table Number of Votes 17 9 7 First A B C Second B C B Third C A A Did You Know? The “Flawed” Electoral College System When citizens of the United States vote for president, they are actually voting to decide which presidential candidate receives all the electoral votes from their state. The Electoral College is a group from each state who are selected by the voters to represent that state in presidential elections. This system was reached by compromise at the constitutional convention in 1787 between those politicians who wanted a direct election of a president and those who wanted Congress to select a president. The resulting system has the potential for some very interesting results that some people consider flaws. For example, it is possible for a candidate to receive a majority of the popular vote and not get elected. This situation occurred only once in U.S. history. In 1876, Samuel J. Tilden received a majority of the popular vote but lost the election to Rutherford B. Hayes. Four other times a candidate won a plurality of the vote but was not elected president. They were Andrew Jackson (1824), Grover Cleveland (1888), Al Gore (2000), and Hillary Clinton (2016). Americans have been dissatisfied with the Electoral College almost since its inception. In fact, there have been more constitutional amendments proposed to restructure the procedure for electing presidents than for any other purpose. Nonetheless, despite all the dissatisfaction with the Electoral College, the rules regarding it remain identical to when it was first adopted. Hero Images/Alamy Stock Photo
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