Table 22-1
Three long-time friends, Sam, Denise, and Carlos, 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 bowling, 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 statement regarding the Condorcet paradox and the results of pairwise voting by Sam,Denise,and Carlos is most accurate
A)The paradox implies that pairwise voting never produces transitive preferences, and so the voting by Sam, Denise, and Carlos fails to produce transitive preferences.
B)The paradox implies that pairwise voting sometimes (but not always) produces transitive preferences, and the voting by Sam, Denise, and Carlos 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, Denise, and Carlos fails to produce transitive preferences.
D)The paradox implies that pairwise voting almost never produces transitive preferences, but the voting by Sam, Denise, and Carlos does produce transitive preferences.

Question

Table 22-1
Three long-time friends, Sam, Denise, and Carlos, 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 bowling, 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 statement regarding the Condorcet paradox and the results of pairwise voting by Sam,Denise,and Carlos is most accurate
A)The paradox implies that pairwise voting never produces transitive preferences, and so the voting by Sam, Denise, and Carlos fails to produce transitive preferences. 
B)The paradox implies that pairwise voting sometimes (but not always) produces transitive preferences, and the voting by Sam, Denise, and Carlos 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, Denise, and Carlos fails to produce transitive preferences. 
D)The paradox implies that pairwise voting almost never produces transitive preferences, but the voting by Sam, Denise, and Carlos does produce transitive preferences.

Quizplus · Accepted Answer

The Condorcet paradox states that pairwise voting sometimes (but not always) fails to produce transitive preferences. In this case, we can see that the preferences of Sam, Denise, and Carlos are not transitive. For example, if we compare the preferences of Sam and Denise, we see that Sam prefers bowling to dinner and dinner to the movies, while Denise prefers dinner to bowling and bowling to the movies. This means that, according to pairwise voting, they should choose between bowling and dinner, but neither option is preferred by all three individuals. Therefore, the voting by Sam, Denise, and Carlos fails to produce transitive preferences.

Table 22-1 Three Long-Time Friends, Sam, Denise, and Carlos, Are Deciding How