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. Suppose the townspeople vote and choose hockey but the town administrator overrules the vote and chooses football because the town's football team has a chance of winning the state championship. Which of the properties of Arrow's impossibility theorem is violated?

Question

Table 22-8
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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. Suppose the townspeople vote and choose hockey but the town administrator overrules the vote and chooses football because the town's football team has a chance of winning the state championship. Which of the properties of Arrow's impossibility theorem is violated?

Quizplus · Accepted Answer

The Answer of Table 22-8
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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. Suppose the townspeople vote and choose hockey but the town administrator overrules the vote and chooses football because the town's football team has a chance of winning the state championship. Which of the properties of Arrow's impossibility theorem is violated?

Table 22-8 ​

Table 22-8