Table 22-2
Three Longtime Friends-Stephanie, Stella, and Lydia-Are Deciding How

question 47

Multiple Choice

Table 22-2
Three longtime friends-Stephanie, Stella, and Lydia-are deciding how they will spend their Sunday afternoon. They all agree that they should do one of the three things: go to a play, play baseball, or go to a soccer game. They also agree that they will have two pairwise votes to determine how to spend their afternoon, with the majority determining the outcome on each vote. The first, second, and third choices for each person are as indicated in the following table.
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$$\begin{array} { | c | c | c | c | } \hline & \text { Stephanie } & \text { Stella } & \text { Lydia } \\\hline \text { First choice } & \text { soccer game } & \text { baseball } & \text { play } \\\hline \text { Second choice } & \text { baseball } & \text { play } & \text { soccer game } \\\hline \text { Third choice } & \text { play } & \text { soccer game } & \text { baseball } \\\hline\end{array}$$
-Refer to Table 22-2. Which of the following statements is correct regarding the Condorcet paradox and the results of pairwise voting by Stephanie, Stella, and Lydia?

• A)The paradox implies that pairwise voting never produces transitive preferences, and so the voting by Stephanie, Stella, and Lydia fails to produce transitive preferences.
• B)The paradox implies that pairwise voting sometimes (but not always) produces transitive preferences, and the voting by Stephanie, Stella, and Lydia does produce transitive preferences.
• C)The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences, and the voting by Stephanie, Stella, and Lydia fails to produce transitive preferences.
• D)The paradox does not apply to the case at hand, because Stephanie's preferences are not individually transitive.

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