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Homework p. 103 (2, 4, 8, 10, 11, 16, 20). 2. a) $19.20 4. a) $13.50 8. 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, s3 11. a) s2, s3

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Homework p 103 2 4 8 10 11 16 20
Homework p. 103 (2, 4, 8, 10, 11, 16, 20)

2. a) $19.20 4. a) $13.50 8. 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, s3 11. 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

Lone-Divider and Lone-Chooser Methods

Unit 3 – Fair Division


Lone divider method
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 method1
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 method2
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
Example

Demark


Example1
Example

Justin

How do we decide what is fair? Both Liz and Liam think _______ is the only fair piece.


Lone chooser method
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 method1
Lone-Chooser Method

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.


Pineapple or orange
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
Homework

  • Lone-Divider WS

  • P. 109-110( 33, 34)


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