Table 22-1
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 22-1.If the town administrator first asks the citizens to vote for hockey or basketball and then asks them to choose between the winner of the first vote and football,what will be the outcome?

Question

Table 22-1
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 22-1.If the town administrator first asks the citizens to vote for hockey or basketball and then asks them to choose between the winner of the first vote and football,what will be the outcome?

Quizplus · Accepted Answer

First, we need to determine the pairwise preferences for each pair of sports:

- Hockey vs. Basketball: 7-3 (majority prefers hockey)
- Hockey vs. Football: 6-4 (majority prefers hockey)
- Basketball vs. Football: 5-5 (tie)

Next, we need to determine the outcome of the first vote between hockey and basketball. Since the majority prefers hockey, hockey will win the first vote.

Finally, we need to determine the outcome of the second vote between the winner of the first vote (hockey) and football. Since the majority prefers hockey over basketball and hockey over football, the majority also prefers hockey over the winner of the first vote (hockey) and football. Therefore, football will win the second vote.

Overall, the outcome will be that football is the sport that the town can afford to maintain.

Table 22-1 The Citizens of Mayville Are Having a Severe Budget Shortage