Chapter 3, Problem 24E

Four partners are dividing a plot of land among themselves using the lone-divider method. After the divider $D$ divides the land into four shares $s_1$, $s_2$, $s_3$, and $s_4$ the choosers $C_1$, $C_2$, and $C_3$ submit their bids for these shares.

a. Suppose that the choosers bid lists are $C_1:\left\{s_2\right\}$;. $C_2:\left\{s_1,s_3\right\}$; $C_3:\left\{s_2,s_3\right\}$ Find a fair division of the land. Explain why this is the only possible fair division.

b. Suppose that the choosers’ bid lists are $C_1:\left\{s_2\right\}$;. $C_2:\left\{s_1,s_3\right\}$; $C_3:\left\{s_1,s_4\right\}$ Describe three different fair divisions of the land.

c. Suppose that the choosers’ bid lists are. $C_1:\left\{s_2\right\}$;. $C_2:\left\{s_1,s_2,s_3\right\}$; $C_3:\left\{s_2,s_3,s_4\right\}$ Describe three different fair divisions of the land.