Table 22-1
Three longtime friends-Sam, Diane, and Cliff-are deciding how they will spend their Saturday evening. They all agree that they should do one of three things: go to a movie, go to a concert, or go out to dinner. 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 22-1.Which of the following statements is correct regarding the Condorcet paradox and the results of pairwise voting by Sam,Diane,and Cliff?
A)The paradox implies that pairwise voting never produces transitive preferences, and so the voting by Sam, Diane, and Cliff fails to produce transitive preferences.
B)The paradox implies that pairwise voting sometimes (but not always) produces transitive preferences, and the voting by Sam, Diane, and Cliff does produce transitive preferences.
C)The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences, and the voting by Sam, Diane, and Cliff fails to produce transitive preferences.
D)The paradox does not apply to the case at hand, because Diane's preferences are not individually transitive.

Question

Table 22-1
Three longtime friends-Sam, Diane, and Cliff-are deciding how they will spend their Saturday evening. They all agree that they should do one of three things: go to a movie, go to a concert, or go out to dinner. 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 22-1.Which of the following statements is correct regarding the Condorcet paradox and the results of pairwise voting by Sam,Diane,and Cliff?
A)The paradox implies that pairwise voting never produces transitive preferences, and so the voting by Sam, Diane, and Cliff fails to produce transitive preferences. 
B)The paradox implies that pairwise voting sometimes (but not always) produces transitive preferences, and the voting by Sam, Diane, and Cliff does produce transitive preferences. 
C)The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences, and the voting by Sam, Diane, and Cliff fails to produce transitive preferences. 
D)The paradox does not apply to the case at hand, because Diane'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. In this case, the voting by Sam, Diane, and Cliff fails to produce transitive preferences because there is a cycle in the preferences: Sam prefers dinner to a concert, Diane prefers a concert to a movie, and Cliff prefers a movie to dinner. This means that the outcome of the voting can depend on the order in which the choices are voted on, instead of being a clear preference order. Therefore, the Condorcet paradox applies to this case.

Table 22-1 Three Longtime Friends-Sam, Diane, and Cliff-Are Deciding How They Will