Terry, Sean, and Nora want to share a cake that is half lemon and half vanilla. Terry pr...

Terry, Sean, and Nora want to share a cake that is half lemon and half vanilla. Terry prefers lemon to vanilla in a 3-to-1 ratio. Sean’s lemon-to-vanilla preference ratio is 3 to 2. Nora values lemon over vanilla in a ratio of 4 to 1. They will use the lone-chooser method, and Nora will be the lone chooser. See problem 45 for details about the lone-chooser method.

a. Terry and Sean are the dividers. If Terry cuts the cake into the following portions, which portion does Sean select?

b. Terry and Sean are the dividers. If Sean cuts the cake into the following portions, which portion does Terry select?

c. Verify that the portions all players end up with from parts (a) and (b) are fair shares according to their own values.

Problem45:

This section discussed fair-division methods for continuous problems, in which one player was the divider, as in the divide-and-choose method for two or three players, and also in which each player had a chance to act as the divider and the chooser, as in the last-diminisher method. Another fair-division method for three players is called the lone-chooser method. In this case, two players divide the cake into two pieces using the divide-and-choose method. Each of the dividers then cuts his or her piece of cake into what he or she feels are three equally valued pieces. The player who is the lone chooser will select one piece from each divider. Explain how this results in a fair division of the cake.