Homework p. 103 (2, 4, 8, 10, 11, 16, 20) 2. a) $ a) $ 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% c) No

Lone-Divider and Lone- Chooser Methods Unit 3 – Fair Division

Lone-Divider Method Three players, one player is the divider, the other two are choosers We will refer to the divider as ____ and the choosers as _____ and _____ This method is an extension of the ______ ______________________ for three people

Lone-Divider Method 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

Lone-Divider Method 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? _________________

Example s1s1 s2s2 s3s3 Angelia Brittany Demark

Example s1s1 s2s2 s3s3 Liz Liam Justin How do we decide what is fair? Both Liz and Liam think _______ is the only fair piece.

Lone-Chooser Method One player is a chooser, the other players are dividers The chooser will be called ____, the dividers will be called ____ and ______.

Lone-Chooser Method Step 1: (_____________) D 1 and D 2 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.

Pineapple or Orange? 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

Homework Lone-Divider WS P ( 33, 34)