Fair Division - Lone Chooser Method - Edubirdie

University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2012
Views:

419

Pages:

1
Author:

Paul Howell

Fair Division Fair Division The LoneLone-Chooser Method for Three Players – Preliminaries. We have one chooser and two dividers. Let’s call the chooser C and the dividers D1 and D2 . As usual, we decide who is what by a random draw. 3.4 The LoneChooser Method 24 23 Fair Division – Fair Division The LoneLone-Chooser Method for Three Players – Step 1 ( Division). D1 and D2 divide S between themselves into two fair shares. To do this, they use the divider-chooser method. Let’s say that D1 ends with S1 and D2 ends with S2 . 25 The LoneLone-Chooser Method for Three Players Step 2 (Subdivision). Each divider divides his or her share into three subshares. Thus D1 divides S1 into three subshares, which we will call S1a, S1b and S1c . Likewise, D2 divides S2 into three subshares, which we will call S2a, S2b and S2c . 26 Fair Division – The LoneLone-Chooser Method for Three Players Step 3 (Selection). The chooser C now selects one of D1 ‘s three subshares and one of D2 ‘s three subshares. These two subshares make up C’s final share. D1 then keeps the remaining two subshares from S1 , and D2 keeps the remaining two subshares from S2 . 27 1

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