Problem

Three teenagers have access to the family car for a few hours each week. The car is avai...

Three teenagers have access to the family car for a few hours each week. The car is available before school on some days, after school on some days, and for a few hours on the weekend. Janice divides the available time into what she believes are three fair plans: plan I, plan II, and plan III. Jill and Jayce judge the fairness of each plan.

a. Suppose that Jill thinks plan I and plan II are acceptable, while Jayce thinks plan III is acceptable. Describe a fair division of the time among Janice, Jill, and Jayce.

b. Suppose that both Jill and Jayce believe plans I and II are acceptable. Describe a fair division of the time among Janice, Jill, and Jayce.

c. Suppose that both Jill and Jayce believe that plan I is the only fair plan. Explain how the process that leads to a fair division may cause Janice to value her piece less than she values one of Jill’s or Jayce’s pieces.

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