Homework p. 103 (2, 4, 8, 10, 11, 16, 20). 2. a) $19.204. a) $13.508. a) s2, s3 ($7 is fair) b) $4.80 b) $4.50 b) s1, s2 ($6 is fair) c) $6.40 c) $5.40 c) s1 ($7 is fair) d) $1.20 d) $1.35 d) A-s3, B-s2, C-s1 10. a) s2, s311. a) s2, s3
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2. a) $19.204. a) $13.508. a) s2, s3 ($7 is fair)
b) $4.80 b) $4.50 b) s1, s2 ($6 is fair)
c) $6.40 c) $5.40 c) s1 ($7 is fair)
d) $1.20 d) $1.35 d) A-s3, B-s2, C-s1
10. a) s2, s311. a) s2, s3
b) s2, s3 b) s1, s2, s3, s4
c) s2, s3 c) s1, s2
d) No, s1 is not fair for anyone d) s1
e) D-s1, C-s2, B-s4, A-s3
16. a) s1[0, 3], s2 [3,12]20. a) No
b) Jared wants s2, $7 worth b) yes, David chooses s2, 60%
Lone-Divider and Lone-Chooser Methods
Unit 3 – Fair Division
______________________ for three people
Step 1: (__________) The divider D divides the cake into three shares (s1, s2, s3).
*D will get one of the three shares, but does not know which share he/she will get. All three shares are equal in the eyes of D
Step 2: (___________) C1 and C2 declare which of the three pieces are fair shares to each of them secretly.
*A chooser’s bid must list every single piece that he/she considers to be a fair share
Step 3: (________________) Who gets which piece?
*Take a look at the bids, who consider’s which pieces to be fair?
*If three people are dividing S, what percentage is a fair share? _________________
How do we decide what is fair? Both Liz and Liam think _______ is the only fair piece.
Step 1: (_____________) D1 and D2 divide S into two fair shares. Use the Divider-Chooser method to do so.
Step 2: (_____________) Each divider divides his share into three sub shares(s1a, s1b, s1c) and (s2a, s2b, s2c).
Step 3: (_____________) The chooser C selects one of D1’s three sub shares and one of D2’s three sub shares. These two shares make up C’s final share.
I will now pass out pineapple/orange cakes to each group of 3. Each person will receive their preference, keep it a secret.
For scenario #1, player 3 will be the chooser.
For scenario #2, player 2 will be the chooser