Table 22-8
The citizens of Mayville are having a severe budget shortage and are faced with eliminating athletics from the town high school. The town administrator has determined that the town can afford to maintain one sport. 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 22-8. The town administrator is a huge basketball fan. If he wants to ensure that basketball is the winning sport, how should he set up the voting?
A)First vote: hockey vs. basketball; Second vote: winner of first vote vs. football
B)First vote: hockey vs. football; Second vote: winner of first vote vs. basketball
C)First vote: basketball vs. football; Second vote: winner of first vote vs. hockey
D)It is impossible for basketball to win according to Arrow's impossibility theorem.

Question

Table 22-8
The citizens of Mayville are having a severe budget shortage and are faced with eliminating athletics from the town high school. The town administrator has determined that the town can afford to maintain one sport. 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 22-8. The town administrator is a huge basketball fan. If he wants to ensure that basketball is the winning sport, how should he set up the voting?
A)First vote: hockey vs. basketball; Second vote: winner of first vote vs. football 
B)First vote: hockey vs. football; Second vote: winner of first vote vs. basketball 
C)First vote: basketball vs. football; Second vote: winner of first vote vs. hockey 
D)It is impossible for basketball to win according to Arrow's impossibility theorem.

Quizplus · Accepted Answer

Setting up the voting as hockey vs. football first ensures that basketball will be pitted against the weaker team in the second vote. If basketball wins that second vote, it will be the winning sport. This strategy takes advantage of the fact that basketball is preferred by a majority over hockey, but not over football.

Table 22-8 The Citizens of Mayville Are Having a Severe Budget Shortage