Chapter 3, Problem 28E

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 the following bids: $C_1:\left\{s_3,s_4\right\}$; $C_2:\left\{s_4\right\}$; $C_3:\left\{s_3\right\}$. For each of the following possible divisions, determine if it is a fair division or not. If not, explain why not.

a. $D$ gets $s_1$; $s_2$, $s_3$, and $s_4$ are recombined into a single piece that is then divided fairly among $C_1$, $C_2$ and $C_3$ using the lone-divider method for three players.

b. $D$ gets $s_3$; $s_1$, $s_2$, and $s_4$ are recombined into a single piece that is then divided fairly among $C_1$, $C_2$, and $C_3$ using the lone-divider method for three players.

c. $D$ gets $s_2$; $s_1$, $s_3$, and $s_4$ are recombined into a single piece that is then divided fairly among $C_1$, $C_2$, and $C_3$ using the lone-divider method for three players.

d. $C_2$ gets $s_4$; $C_3$ gets $s_3$; $s_1$, $s_2$ are recombined into a single piece that is then divided fairly between $C_1$ and $D$ using the divider-chooser method.