Warm Up – 2/20 - Thursday
A) How much more does Angela like
strawberry than vanilla?
B) Give a percentage that describes
how much Angela values the Vanilla
portion.
C) What percentage of the cake
would Angela consider a 60 degree
slice of vanilla?
D) A 30 degree slice of strawberry?
Chapter so Far
• Fair Division Criteria
– Everyone needs to be satisfied in order for a
division to be fair.
• Divider-Chooser – 2 players
– The divider tries to make both sides exactly 50%
so they are guaranteed a fair share.
– The chooser gets the better deal as they may get a
fair division over 50%.
Lone-Divider Method
• Lone-Divider is very similar to Divider-Chooser
except now we have more than two players.
• The Rules
1. One player is randomly selected to divide
(they want a fair share!)
2. The other players submit a bid set (a list of
the pieces they think are fair)
3. The goodies are distributed fairly and
optimally if possible.
Lone-Divider
• Who was the divider in this case?
• Give the other two players bid sets.
• Distribute the goods fairly.
Lone-Divider
We call the pieces the other
two players want C-Pieces!
Lone-Divider
Changed the table slightly
• A) Who was the divider?
• B) Give the other players’ bid sets.
• C) Create an optimal distribution if possible.
Example 3
• A) Who was the divider?
• B) Give the other players’ bid sets.
• C) Create an optimal distribution if possible.
Table 2
The only C-piece is 𝑠3 . Because neither Cindy or Cher wants 𝑠1
Everyone agrees to give that piece to Dale (Dale is fine with this!).
Cindy and Cher are left trying to decide what to do about 𝑠3 and 𝑠2 .
How would you handle this in real life, Ryan?
Final Outcome
• Dale will get 𝑠1 .
• Cindy and Cher will reexamine 𝑠2 and 𝑠3 and
use the Divider-Chooser method for two
players to divide the rest.
• Answer you need to put:
• Dale gets 𝑠1 . Cindy and Cher use DividerChooser on 𝑠2 and 𝑠3 .