Table 22-2
Three longtime friends-Allen, Brian, and Cody-are deciding how they will spend their Sunday afternoon. They all agree that they should do one of three things: go to a movie, play golf, or go to a baseball 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 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 Allen, Brian, and Cody?
A)The paradox implies that pairwise voting never produces transitive preferences, and so the voting by Allen, Brian, and Cody fails to produce transitive preferences.
B)The paradox implies that pairwise voting sometimes (but not always) produces transitive preferences, and the voting by Allen, Brian, and Cody does produce transitive preferences.
C)The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences, and the voting by Allen, Brian, and Cody fails to produce transitive preferences.
D)The paradox does not apply to the case at hand, because Brian's preferences are not individually transitive.

Question

Table 22-2
Three longtime friends-Allen, Brian, and Cody-are deciding how they will spend their Sunday afternoon. They all agree that they should do one of three things: go to a movie, play golf, or go to a baseball 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 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 Allen, Brian, and Cody?
A)The paradox implies that pairwise voting never produces transitive preferences, and so the voting by Allen, Brian, and Cody fails to produce transitive preferences. 
B)The paradox implies that pairwise voting sometimes (but not always) produces transitive preferences, and the voting by Allen, Brian, and Cody does produce transitive preferences. 
C)The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences, and the voting by Allen, Brian, and Cody fails to produce transitive preferences. 
D)The paradox does not apply to the case at hand, because Brian's preferences are not individually transitive.

Quizplus · Accepted Answer

The Condorcet paradox implies that pairwise voting may fail to produce transitive preferences, and in this case, the voting by Allen, Brian, and Cody does fail to produce transitive preferences. This can be seen by looking at the pairwise votes: Allen beats Brian, Brian beats Cody, and Cody beats Allen. Therefore, whichever option is chosen will not have majority support over both of the other options.

Table 22-2 Three Longtime Friends-Allen, Brian, and Cody-Are Deciding How They Will