Table 22-7
Suppose that residents of a town are asked to vote on the best way to improve the safety of an intersection. The three choices are: a stoplight, a 4-way stop, and a 2-way stop. The voters are divided into three groups based on their preferences.
Voter Type
-Refer to Table 22-7. Which of the following statements is correct regarding the Condorcet paradox and the results of pairwise voting on how to improve the safety of the intersection?
A)The paradox implies that pairwise voting never produces transitive preferences, and so the voting in the town fails to produce transitive preferences.
B)The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences, but the voting in the town does produce transitive preferences.
C)The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences, and the voting in the town fails to produce transitive preferences.
D)The paradox implies that pairwise voting always produces transitive preferences, and so the voting in the town produces transitive preferences.

Question

Table 22-7
Suppose that residents of a town are asked to vote on the best way to improve the safety of an intersection. The three choices are: a stoplight, a 4-way stop, and a 2-way stop. The voters are divided into three groups based on their preferences.
Voter Type 
-Refer to Table 22-7. Which of the following statements is correct regarding the Condorcet paradox and the results of pairwise voting on how to improve the safety of the intersection?
A)The paradox implies that pairwise voting never produces transitive preferences, and so the voting in the town fails to produce transitive preferences. 
B)The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences, but the voting in the town does produce transitive preferences. 
C)The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences, and the voting in the town fails to produce transitive preferences. 
D)The paradox implies that pairwise voting always produces transitive preferences, and so the voting in the town produces transitive preferences.

Quizplus · Accepted Answer

The Condorcet paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences. In this case, if voters are asked to choose between a stoplight and a 2-way stop, the majority prefers a stoplight (31 to 19) and if they are asked to choose between a 2-way stop and a 4-way stop, the majority prefers a 4-way stop (38 to 12). However, if voters are asked to choose between a stoplight and a 4-way stop, the majority prefers a 2-way stop (33 to 17). This implies that the group preferences are not transitive. The voting in the town does produce transitive preferences since there is a majority preference for the 4-way stop, followed by the stoplight, and then the 2-way stop. Therefore, the best choice is B.

Table 22-7 Suppose That Residents of a Town Are Asked to Vote