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.
Which voting methods can produce ties? pg. 153 How can ties be broken? pg. 153
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The four voting systems we have examined can produce different winners even when the same voter preference table is used. For example, using exactly the same preference table, Alice was selected as department chair in Example 3.4, while Carlos was selected as department chair in Example 3.6. Any of these methods can also produce a tie between two or more of the alternatives. In some cases, voter preferences are perfectly balanced, and a tie is in the nature of things (for example, when there are two alternatives, an even number of voters, and exactly the same number of supporters for each alternative). The only way to break a tie caused by perfectly balanced support is either to make an arbitrary choice (such as by flipping a coin) or to bring in another voter. For example, the Vice President of the United States is President of the U.S. Senate, but has a vote in the Senate only when the rest of the Senate is deadlocked.
Sometimes a tie can be broken in a more rational fashion than by a coin flip. For example, if the Borda count method is used, then it may be possible to break a tie based on which candidate obtained the most first-place rankings. Choosing different tiebreaking methods can result in different winners, so the proper thing to do is decide in advance on a tie-breaking method.
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