1. Warm Up – 2/24 - Monday
Five players are dividing a cake using the lone-
Divider Method. 𝑃 5 divides the cake. The bid sets
are as follows.
𝑃 1 − 𝑠 2 , 𝑠 4
𝑃 2 − 𝑠 2 , 𝑠 4
𝑃 3 − 𝑠 2 , 𝑠 3 , 𝑠 5
𝑃 4 −{ 𝑠 2 , 𝑠 3 , 𝑠 4 }
What is 𝑃 5 ’s bidset?
Which slice does 𝑃 3 have to take? Why?
How many fair divisions can be made? Why no
more?

2. Chapter So-Far Fair Division Divider-Chooser (2 players)
Fair means everyone gets what a fair share based on their own value system
Divider-Chooser (2 players)
Lone Divider (More than 2 players)
One person divides, the other players bid
Ties are settled by Divider-Chooser
Lone Chooser (More than 2 players)
One person chooses at the end
Other Players ensure they get at least a fair share

3. Lone-Chooser Example
Angela, Boris, and Carlos will split a strawberry-vanilla cake using Lone-Chooser.
Above is how they value the cake.
Label each side of the cake in terms of how much the person likes that side.

4. Angela cuts the cake…
Into two shares, 𝑠 ° 𝑜𝑓 𝑠𝑡𝑟𝑎𝑤𝑏𝑒𝑟𝑟𝑦 and 𝑠 2 (60° 𝑠𝑡𝑟𝑎𝑤𝑏𝑒𝑟𝑟𝑦, 180° 𝑣𝑎𝑛𝑖𝑙𝑙𝑎).
1. Which share will Boris pick?
2. How will Boris subdivide his share?
3. How will Angela subdivide her share?
4. Which pieces will Carlos select?

5. Lone-Chooser Classwork