Table 22-3
The citizens of Paradoxopolis will decide whether to build a new school,build a new park,or build a new road.Exactly one of the three choices will prevail,and the choice will be made by way of pairwise voting,with the majority determining the outcome on each vote.The preferences of the voters are summarized in the table below.

-Refer to Table 22-3.Which of the following statements is correct regarding the Condorcet paradox and the results of pairwise voting in Paradoxopolis?
A) The paradox implies that pairwise voting never produces transitive preferences,and so the voting in Paradoxopolis fails to produce transitive preferences.
B) The paradox implies that pairwise voting sometimes (but not always)produces transitive preferences,and the voting in Paradoxopolis does produce transitive preferences.
C) The paradox implies that pairwise voting sometimes (but not always)fails to produce transitive preferences,and the voting in Paradoxopolis fails to produce transitive preferences.
D) The paradox does not apply to the case at hand,because the preferences of Type 3 voters are not individually transitive.

Question

Table 22-3
The citizens of Paradoxopolis will decide whether to build a new school,build a new park,or build a new road.Exactly one of the three choices will prevail,and the choice will be made by way of pairwise voting,with the majority determining the outcome on each vote.The preferences of the voters are summarized in the table below.
 
-Refer to Table 22-3.Which of the following statements is correct regarding the Condorcet paradox and the results of pairwise voting in Paradoxopolis?
A) The paradox implies that pairwise voting never produces transitive preferences,and so the voting in Paradoxopolis fails to produce transitive preferences. 
B) The paradox implies that pairwise voting sometimes (but not always)produces transitive preferences,and the voting in Paradoxopolis does produce transitive preferences. 
C) The paradox implies that pairwise voting sometimes (but not always)fails to produce transitive preferences,and the voting in Paradoxopolis fails to produce transitive preferences. 
D) The paradox does not apply to the case at hand,because the preferences of Type 3 voters are not individually transitive.

Quizplus · Accepted Answer

The Condorcet paradox occurs when pairwise voting produces non-transitive preferences. This means that the majority preference between two options can change depending on which option is voted on first. In Paradoxopolis, the preferences of the voters are non-transitive, as seen in the table. Thus, the pairwise voting may sometimes fail to produce transitive preferences. Therefore, option C is the correct choice.

Table 22-3 the Citizens of Paradoxopolis Will Decide Whether to Build a Build