The Lone-Chooser Method
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1 The Lone-Chooser Method Lecture 11 Section 3.3 Robb T. Koether Hampden-Sydney College Fri, Sep 19, 2014 Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
2 1 Assignment 2 The Lone-Chooser Method 3 Example 3 Players Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
3 Outline 1 Assignment 2 The Lone-Chooser Method 3 Example 3 Players Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
4 Assignment Assignment Page 96: Exercises 35, 36, 37, 38. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
5 Outline 1 Assignment 2 The Lone-Chooser Method 3 Example 3 Players Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
6 The Lone-Chooser Method Definition (The Lone-Chooser Method) In the lone-chooser method, one player is designated to be the chooser. The other players (the dividers) divide the assets among themselves. (They may use the lone-divider method). Then each of the dividers divides his share into equal subshares. The chooser then chooses one subshare from each of the dividers. The dividers keep the subshares that are left. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
7 The Lone-Chooser Method Assets John Joe Jim The players and the assets. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
8 The Lone-Chooser Method Share 1 Share 2 John (lone chooser) Joe Jim John is the lone chooser. Joe and Jim use divider-chooser method. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
9 The Lone-Chooser Method Share 1 Share 2 John (lone chooser) Joe Jim Joe divides. Jim chooses. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
10 The Lone-Chooser Method Share 1 Share 2 John (lone chooser) Joe Jim Joe has Share 1. Jim has Share 2. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
11 The Lone-Chooser Method Subshare 1 Subshare 2 Subshare 1 Subshare 3 Subshare 3 Subshare 2 John (lone chooser) Joe Jim Joe and Jim subdivide their shares. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
12 The Lone-Chooser Method Subshare 1 Subshare 2 Subshare 1 Subshare 3 Subshare 3 Subshare 2 John (lone chooser) Joe Jim John chooses one subshare from each. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
13 The Lone-Chooser Method Subshare 1 Subshare 2 Subshare 1 Subshare 3 Subshare 2 Subshare 3 John (lone chooser) Joe Jim Everybody is happy. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
14 The Lone-Chooser Method Subshare 1 Subshare 2 Subshare 1 Subshare 3 Subshare 2 Subshare 3 John (lone chooser) Joe Jim How come? Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
15 Outline 1 Assignment 2 The Lone-Chooser Method 3 Example 3 Players Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
16 Example Example (The Lone-Chooser Method 3 Players) John, Joe, and Jim are dividing 4 pies: apple, cherry, lemon, and pecan. The value systems of the players are as follows. Apple Cherry Lemon Pecan Fair Share John Joe Jim Jim is the lone-chooser. John and Joe use the divider-chooser method, with John the divider. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
17 Example Example (The Lone-Chooser Method 3 Players) John divides into Share 1 = Apple + Cherry (value 18). Share 2 = Lemon + Pecan (value 18). Joe chooses Share 2 (value 12) over Share 1 (value 9). John gets Share 1. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
18 Example Example (The Lone-Chooser Method 3 Players) John divides Share 1 into subshares. Subshare 1 = 1 2 Apple (value 6). Subshare 2 = 1 2 Apple (value 6). Subshare 3 = 1 3 Apple + Cherry (value 6). Joe divides Share 2 into subshares. Subshare 1 = 1 2 Lemon (value 4). Subshare 2 = 1 2 Lemon (value 4). Subshare 3 = Pecan (value 4). Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
19 Example Example (The Lone-Chooser Method 3 Players) Jim values John s subshares as follows. Subshare 1 has value 3. Subshare 2 has value 3. Subshare 3 has value 4. Jim values Joe s subshares as follows. Subshare 1 = has value 1. Subshare 2 = has value 1. Subshare 3 = has value 6. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
20 Example Example (The Lone-Chooser Method 3 Players) Jim chooses Subshare 3 from John and Subshare 3 from Joe, for a value of 10. John is left with his Subshares 1 and 2, for a value of 12. Joe is left with his Subshares 1 and 2, for a value of 8. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
21 Example Example (The Lone-Chooser Method 3 Players) What if Jim were the first divider, John the first chooser, and then Jim and John the subdividers and Joe the second chooser? What if Joe were the first divider, Jim the first chooser, and then Joe and Jim the subdividers and John the second chooser? In general, which role would you prefer to be in? Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
22 Example Example (The Lone-Chooser Method 4 Players) John, Joe, Jim, and Jack are dividing 3 pies: apple, cherry, and lemon. Their value systems are as follows. Apple Cherry Lemon Fair Share John Joe Jim Jack First, John divides in halves and Joe chooses. Second, John and Joe divide into thirds and Jim chooses. Finally, John, Joe, and Jim divide into fourth and Jack chooses. Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Fri, Sep 19, / 15
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