Table 22-2
Three longtime friends-Jack, Ryan, and Colin-are deciding how they will spend their Sunday afternoon. They all agree that they should do one of three things: go to a movie, go to the zoo, or go to a museum. They also agree that they will have two pairwise votes to determine how to spend their evening, with the majority determining the outcome on each vote. The first, second, and third choices for each person are as indicated in the table below.

-Refer to Table 22-2.Which of the following statements is correct regarding the Condorcet paradox and the results of pairwise voting by Jack,Ryan,and Colin?
A) The paradox implies that pairwise voting never produces transitive preferences, and so the voting by Jack, Ryan, and Colin fails to produce transitive preferences.
B) The paradox implies that pairwise voting sometimes (but not always) produces transitive preferences, and the voting by Jack, Ryan, and Colin does produce transitive preferences.
C) The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences, and the voting by Jack, Ryan, and Colin fails to produce transitive preferences.
D) The paradox does not apply to the case at hand, because Ryan's preferences are not individually transitive.

Question

Table 22-2
Three longtime friends-Jack, Ryan, and Colin-are deciding how they will spend their Sunday afternoon. They all agree that they should do one of three things: go to a movie, go to the zoo, or go to a museum. They also agree that they will have two pairwise votes to determine how to spend their evening, with the majority determining the outcome on each vote. The first, second, and third choices for each person are as indicated in the table below.
 
-Refer to Table 22-2.Which of the following statements is correct regarding the Condorcet paradox and the results of pairwise voting by Jack,Ryan,and Colin?
A) The paradox implies that pairwise voting never produces transitive preferences, and so the voting by Jack, Ryan, and Colin fails to produce transitive preferences. 
B) The paradox implies that pairwise voting sometimes (but not always) produces transitive preferences, and the voting by Jack, Ryan, and Colin does produce transitive preferences. 
C) The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences, and the voting by Jack, Ryan, and Colin fails to produce transitive preferences. 
D) The paradox does not apply to the case at hand, because Ryan's preferences are not individually transitive.

Quizplus · Accepted Answer

The Condorcet paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences, and the voting by Jack, Ryan, and Colin fails to produce transitive preferences. This is because there is no clear majority preference in either pairwise vote, so the resulting choices are not transitive. For example, Jack prefers the museum to the zoo and the zoo to the movie, while Ryan prefers the movie to the zoo and the zoo to the museum. If Jack and Ryan vote on museum vs. movie, Ryan wins with 2 votes to 1. If Jack and Colin vote on museum vs. zoo, Jack wins with 2 votes to 1. Therefore, if a final vote is held between the zoo and the movie, it is unclear which choice should win since there is no consistent majority preference.

Table 22-2 Three Longtime Friends-Jack, Ryan, and Colin-Are Deciding How They Will