Table 22-2
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 22-2.Which of the following statements is correct?
A)In a pairwise election, "school" beats "road."
B)In a pairwise election, "road" beats "park."
C)In a pairwise election, "school" beats "park."
D)All of the above are correct.

Question

Table 22-2
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 22-2.Which of the following statements is correct?
A)In a pairwise election, "school" beats "road." 
B)In a pairwise election, "road" beats "park." 
C)In a pairwise election, "school" beats "park." 
D)All of the above are correct.

Quizplus · Accepted Answer

In a pairwise election, "school" beats "park" because 45+15 = 60 voters prefer "school" over "park", while only 40 voters prefer "park" over "school". Similarly, in a pairwise election, "road" beats "park" because 55+5 = 60 voters prefer "road" over "park", while only 40 voters prefer "park" over "road". However, "school" and "road" are tied at 50 voters each in a pairwise election, so the final outcome cannot be determined without further voting or alternative methods such as instant-runoff voting.

Table 22-2 the Citizens of Paradoxopolis Will Decide Whether to Build a Build