Jason, Kelly, and Lauren use the Lone Chooser method to divide use of a retail space over the course of a year.Jason is the Chooser (the overall Chooser in the Lone Chooser method), and Lauren is the first Divider.Each runs a different type of business.Their individual preferences are as follows:

Jason values the each month of the year equally.

Kelly values only the months in the first half of the year (and values each one equally); she has no use for the retail space in the second half of the year.

Lauren values each month in the first half of the year twice as much as each month in the second half.

Division:

a.Where does Lauren make the first division, i.e., at what point in the year?

b.If we call the two shares into which Lauren has divided the year s₁ and s₂, how much are each of s₁ and s₂ worth to Kelly, as a fraction (or percentage) of what the whole year is worth?

c. Describe Kelly's share (i.e., which share does she select) and Lauren's share (which share is she left with) at the end of the division stage.

Subdivision:

d.Describe the second division which Kelly makes, i.e., describe (in terms of specific months or parts of months) the 3 subshares k₁, k₂, k₃ she creates from her share, and indicate how much each subshare is worth to her. You may describe the value to Kelly in terms of "Kelly points", or as a fraction of the value of the whole year.

e.Describe the second division which Lauren makes, i.e., describe (in terms of specific months or parts of months) the 3 subshares l₁, l₂, l₃ she creates from her share, and indicate how much each subshare is worth to her.You may describe the value to Lauren in terms of "Lauren points", or as a fraction of the value of the whole year.

Selection: Now Jason, the Chooser, returns.

f. In the following table, write down how much each subshare of Kelly's is worth to Jason, and how much each subshare of Lauren's is worth to Jason.You may describe the value to Jason in terms of "Jason points", or as a fraction of the value of the whole year.

g.Which subshares does Jason select?

h.By filling out the following table, describe the final fair division of the year (indicating which months each player receives), and find the value of each player's final share as a fraction (or percentage) of the value of the entire year: