Scenario 22-4
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 Scenario 22-4.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

Scenario 22-4
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 Scenario 22-4.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 states that a situation can arise where the majority prefers A over B, B over C, and C over A. This results in pairwise voting sometimes failing to produce transitive preferences. In this scenario, we can see that Group 1 prefers the stoplight, Group 2 prefers the 4-way stop, and Group 3 prefers the 2-way stop. However, when we compare the options pairwise, we can see that the stoplight beats the 4-way stop, the 4-way stop beats the 2-way stop, but the 2-way stop beats the stoplight. This is an example of the Condorcet paradox, but since the majority of voters prefer the 4-way stop over the other two choices, it can be considered the best choice. Therefore, the correct answer is B.

Scenario 22-4 Suppose That Residents of a Town Are Asked to Vote