The Lone-Chooser Method - H-SC

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The Lone-Chooser MethodLecture 16Section 3.4Robb T. KoetherHampden-Sydney CollegeWed, Oct 3, 2018Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20181 / 23

1The Lone-Chooser Method2Example – 3 Players3Example – 4 Players4AssignmentRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20182 / 23

Outline1The Lone-Chooser Method2Example – 3 Players3Example – 4 Players4AssignmentRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20183 / 23

The Lone-Chooser MethodDefinition (The Lone-Chooser Method)In the lone-chooser method,One player is designated to be the chooser.The other players are the dividers. They divide the assets amongthemselves (details to follow).Then each of the dividers divides his share into equal subshares.The chooser then chooses one subshare from each of thedividers.The dividers keep the subshares that are left.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20184 / 23

The Lone-Chooser MethodThis is normally done in a recursive manner.For example, if there are 4 players A, B, C, and D.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20185 / 23

The Lone-Chooser MethodThis is normally done in a recursive manner.For example, if there are 4 players A, B, C, and D.A starts off with all the assets.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20185 / 23

The Lone-Chooser MethodThis is normally done in a recursive manner.For example, if there are 4 players A, B, C, and D.A starts off with all the assets.Then A divides them into 2 equal shares. B chooses one of them.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20185 / 23

The Lone-Chooser MethodThis is normally done in a recursive manner.For example, if there are 4 players A, B, C, and D.A starts off with all the assets.Then A divides them into 2 equal shares. B chooses one of them.Then A and B each divide their shares into 3 equal subshares.Player C chooses one subshare from each.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20185 / 23

The Lone-Chooser MethodThis is normally done in a recursive manner.For example, if there are 4 players A, B, C, and D.A starts off with all the assets.Then A divides them into 2 equal shares. B chooses one of them.Then A and B each divide their shares into 3 equal subshares.Player C chooses one subshare from each.Then A, B, and C each divide their shares into 4 equal subshares.Player D chooses one subshare from each.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20185 / 23

The Lone-Chooser MethodABCDA starts with all the assetsRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20186 / 23

The Lone-Chooser MethodABCDA divides them into 2 equal sharesRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20186 / 23

The Lone-Chooser MethodABCDB chooses one of the sharesRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20186 / 23

The Lone-Chooser MethodABCDA and B divide their assets into 3 equal subsharesRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20186 / 23

The Lone-Chooser MethodABCDC chooses one subshare from eachRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20186 / 23

The Lone-Chooser MethodABCDA, B, and C divide their assets into 4 equal subsharesRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20186 / 23

The Lone-Chooser MethodABCDD chooses one subshare from eachRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20186 / 23

Outline1The Lone-Chooser Method2Example – 3 Players3Example – 4 Players4AssignmentRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20187 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Andy, Bob, and Chuck are dividing 4 pies: apple, cherry, lemon,and pecan.The value systems of the players are as an846Chuck is the lone-chooser.But in the meantime, Andy and Bob divide the assets between thetwo of them, with Andy the divider and Bob the lone chooser.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20188 / 23

ExampleExample (The Lone-Chooser Method – 3 an846How should Andy divide all the assets into two equal shares?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20189 / 23

ExampleExample (The Lone-Chooser Method – 3 an846How should Andy divide all the assets into two equal shares? S1 :A C ( 18.00); S2 : L P ( 18.00)Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20189 / 23

ExampleExample (The Lone-Chooser Method – 3 an846How should Andy divide all the assets into two equal shares? S1 :A C ( 18.00); S2 : L P ( 18.00)Which share should Bob choose?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20189 / 23

ExampleExample (The Lone-Chooser Method – 3 an846How should Andy divide all the assets into two equal shares? S1 :A C ( 18.00); S2 : L P ( 18.00)Which share should Bob choose? S2Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20189 / 23

ExampleExample (The Lone-Chooser Method – 3 an846How should Andy divide all the assets into two equal shares? S1 :A C ( 18.00); S2 : L P ( 18.00)Which share should Bob choose? S2Division so far: Andy has A C; Bob has L P.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 20189 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Now Andy and Bob each divide their shares each into 3 equalsubshares.Andy’s share, Apple and Cherry, to be divided 3 ways and Chuckchooses:Apple CherryAndy126Chuck64Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201810 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Now Andy and Bob each divide their shares each into 3 equalsubshares.Andy’s share, Apple and Cherry, to be divided 3 ways and Chuckchooses:Apple CherryAndy126Chuck64What are Andy’s 3 subshares?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201810 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Now Andy and Bob each divide their shares each into 3 equalsubshares.Andy’s share, Apple and Cherry, to be divided 3 ways and Chuckchooses:Apple CherryAndy126Chuck64What are Andy’s 3 subshares? S1 : 21 A ( 6.00); S2 : 12 A ( 6.00);S3 : C ( 6.00)Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201810 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Now Andy and Bob each divide their shares each into 3 equalsubshares.Andy’s share, Apple and Cherry, to be divided 3 ways and Chuckchooses:Apple CherryAndy126Chuck64What are Andy’s 3 subshares? S1 : 21 A ( 6.00); S2 : 12 A ( 6.00);S3 : C ( 6.00)Which one does Chuck choose?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201810 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Now Andy and Bob each divide their shares each into 3 equalsubshares.Andy’s share, Apple and Cherry, to be divided 3 ways and Chuckchooses:Apple CherryAndy126Chuck64What are Andy’s 3 subshares? S1 : 21 A ( 6.00); S2 : 12 A ( 6.00);S3 : C ( 6.00)Which one does Chuck choose? S3Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201810 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Now Andy and Bob each divide their shares each into 3 equalsubshares.Andy’s share, Apple and Cherry, to be divided 3 ways and Chuckchooses:Apple CherryAndy126Chuck64What are Andy’s 3 subshares? S1 : 21 A ( 6.00); S2 : 12 A ( 6.00);S3 : C ( 6.00)Which one does Chuck choose? S3Now Andy has Apple and Chuck has Cherry.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201810 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Bob’s share, Lemon and Pecan, to be divided 3 ways and Chuckchooses:Lemon PecanBob84Chuck26Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201811 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Bob’s share, Lemon and Pecan, to be divided 3 ways and Chuckchooses:Lemon PecanBob84Chuck26What are Bob’s 3 subshares?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201811 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Bob’s share, Lemon and Pecan, to be divided 3 ways and Chuckchooses:Lemon PecanBob84Chuck26What are Bob’s 3 subshares? S1 : 21 L ( 4.00); S2 : 12 L ( 4.00);S3 : P ( 4.00)Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201811 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Bob’s share, Lemon and Pecan, to be divided 3 ways and Chuckchooses:Lemon PecanBob84Chuck26What are Bob’s 3 subshares? S1 : 21 L ( 4.00); S2 : 12 L ( 4.00);S3 : P ( 4.00)Which one does Chuck choose?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201811 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Bob’s share, Lemon and Pecan, to be divided 3 ways and Chuckchooses:Lemon PecanBob84Chuck26What are Bob’s 3 subshares? S1 : 21 L ( 4.00); S2 : 12 L ( 4.00);S3 : P ( 4.00)Which one does Chuck choose? S3Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201811 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)Bob’s share, Lemon and Pecan, to be divided 3 ways and Chuckchooses:Lemon PecanBob84Chuck26What are Bob’s 3 subshares? S1 : 21 L ( 4.00); S2 : 12 L ( 4.00);S3 : P ( 4.00)Which one does Chuck choose? S3Final division: Andy gets Apple ( 6.00), Bob gets Lemon ( 8.00),Chuck gets Cherry and Pecan ( 10.00).Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201811 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)What if Chuck were the first divider, Bob the first lone chooser,and then Chuck and Bob the subdividers and Andy the secondlone chooser?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201812 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)What if Chuck were the first divider, Bob the first lone chooser,and then Chuck and Bob the subdividers and Andy the secondlone chooser?What if Bob were the first divider, Andy the first lone chooser, andthen Bob and Andy the subdividers and Chuck the second lonechooser?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201812 / 23

ExampleExample (The Lone-Chooser Method – 3 Players)What if Chuck were the first divider, Bob the first lone chooser,and then Chuck and Bob the subdividers and Andy the secondlone chooser?What if Bob were the first divider, Andy the first lone chooser, andthen Bob and Andy the subdividers and Chuck the second lonechooser?In general, which role would you prefer to be in: first divider, firstlone chooser, or second lone chooser?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201812 / 23

Outline1The Lone-Chooser Method2Example – 3 Players3Example – 4 Players4AssignmentRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201813 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)Andy, Bob, Chuck, and Dave are dividing 3 pies.Their value systems are as 463First, Andy divides into equal halves and Bob chooses.Second, Andy and Bob divide into equal thirds and Chuckchooses.Finally, Andy, Bob, and Chuck divide into equal fourths and Davechooses.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201814 / 23

ExampleExample (The Lone-Chooser Method – 4 463How does Andy divide the assets into two equal shares?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201815 / 23

ExampleExample (The Lone-Chooser Method – 4 463How does Andy divide the assets into two equal shares? S1 : A;S2 : C LRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201815 / 23

ExampleExample (The Lone-Chooser Method – 4 463How does Andy divide the assets into two equal shares? S1 : A;S2 : C LWhich share does Bob choose?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201815 / 23

ExampleExample (The Lone-Chooser Method – 4 463How does Andy divide the assets into two equal shares? S1 : A;S2 : C LWhich share does Bob choose? S2Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201815 / 23

ExampleExample (The Lone-Chooser Method – 4 463How does Andy divide the assets into two equal shares? S1 : A;S2 : C LWhich share does Bob choose? S2Now Andy has Apple and Bob has Cherry and Lemon.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201815 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)AndyChuckApple126Andy has only the Apple pie and now Chuck is the chooer.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201816 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)AndyChuckApple126Andy has only the Apple pie and now Chuck is the chooer.How does Andy divide his asset into three equal subshares?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201816 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)AndyChuckApple126Andy has only the Apple pie and now Chuck is the chooer.How does Andy divide his asset into three equal subshares? S1 :1113 A; S2 : 3 A; S3 : 3 ARobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201816 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)AndyChuckApple126Andy has only the Apple pie and now Chuck is the chooer.How does Andy divide his asset into three equal subshares? S1 :1113 A; S2 : 3 A; S3 : 3 AWhich subshare does Chuck choose?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201816 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)AndyChuckApple126Andy has only the Apple pie and now Chuck is the chooer.How does Andy divide his asset into three equal subshares? S1 :1113 A; S2 : 3 A; S3 : 3 AWhich subshare does Chuck choose? S3 (Or any other. They areidentical.)Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201816 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)AndyChuckApple126Andy has only the Apple pie and now Chuck is the chooer.How does Andy divide his asset into three equal subshares? S1 :1113 A; S2 : 3 A; S3 : 3 AWhich subshare does Chuck choose? S3 (Or any other. They areidentical.)Now Andy has23Apple and Chuck hasRobb T. Koether (Hampden-Sydney College)The Lone-Chooser Method13Apple.Wed, Oct 3, 201816 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)BobChuckCherry88Lemon46So far, Bob has the Cherry and Lemon pies and Chuck is thechooser.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201817 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)BobChuckCherry88Lemon46So far, Bob has the Cherry and Lemon pies and Chuck is thechooser.How does Bob divide his assets into three equal subshares?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201817 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)BobChuckCherry88Lemon46So far, Bob has the Cherry and Lemon pies and Chuck is thechooser.How does Bob divide his assets into three equal subshares?S1 : 21 C; S2 : 21 C; S3 : LRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201817 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)BobChuckCherry88Lemon46So far, Bob has the Cherry and Lemon pies and Chuck is thechooser.How does Bob divide his assets into three equal subshares?S1 : 21 C; S2 : 21 C; S3 : LWhich subshare does Chuck choose?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201817 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)BobChuckCherry88Lemon46So far, Bob has the Cherry and Lemon pies and Chuck is thechooser.How does Bob divide his assets into three equal subshares?S1 : 21 C; S2 : 21 C; S3 : LWhich subshare does Chuck choose? S3Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201817 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)BobChuckCherry88Lemon46So far, Bob has the Cherry and Lemon pies and Chuck is thechooser.How does Bob divide his assets into three equal subshares?S1 : 21 C; S2 : 21 C; S3 : LWhich subshare does Chuck choose? S3Now Andy has 32 Apple, Bob has Cherry (both halves), and Chuckhas 13 Apple and the Lemon.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201817 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)23AndyDaveAndy has only theRobb T. Koether (Hampden-Sydney College)23Apple86of the Apple pie.The Lone-Chooser MethodWed, Oct 3, 201818 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)23AndyDaveAndy has only the23Apple86of the Apple pie.How does Andy divide his asset into four equal subshares?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201818 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)23AndyDaveAndy has only the23Apple86of the Apple pie.How does Andy divide his asset into four equal subshares?S1 : 61 A; S2 : 61 A; S3 : 16 A; S4 : 16 ARobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201818 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)23AndyDaveAndy has only the23Apple86of the Apple pie.How does Andy divide his asset into four equal subshares?S1 : 61 A; S2 : 61 A; S3 : 16 A; S4 : 16 AWhich subshare does Dave choose?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201818 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)23AndyDaveAndy has only the23Apple86of the Apple pie.How does Andy divide his asset into four equal subshares?S1 : 61 A; S2 : 61 A; S3 : 16 A; S4 : 16 AWhich subshare does Dave choose? S4 (Or any other. They areidentical.)Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201818 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)23AndyDaveAndy has only the23Apple86of the Apple pie.How does Andy divide his asset into four equal subshares?S1 : 61 A; S2 : 61 A; S3 : 16 A; S4 : 16 AWhich subshare does Dave choose? S4 (Or any other. They areidentical.)Now Andy has12Apple and Dave hasRobb T. Koether (Hampden-Sydney College)The Lone-Chooser Method16Apple.Wed, Oct 3, 201818 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)BobDaveCherry88Now Bob has only the Cherry pie.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201819 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)BobDaveCherry88Now Bob has only the Cherry pie.How does Bob divide his asset into four equal subshares?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201819 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)BobDaveCherry88Now Bob has only the Cherry pie.How does Bob divide his asset into four equal subshares? S1 : 41 C;S2 : 41 C; S3 : 14 C; S4 : 14 CRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201819 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)BobDaveCherry88Now Bob has only the Cherry pie.How does Bob divide his asset into four equal subshares? S1 : 41 C;S2 : 41 C; S3 : 14 C; S4 : 14 CWhich subshare does Chuck choose?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201819 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)BobDaveCherry88Now Bob has only the Cherry pie.How does Bob divide his asset into four equal subshares? S1 : 41 C;S2 : 41 C; S3 : 14 C; S4 : 14 CWhich subshare does Chuck choose? S4 (Or any other. They areidentical.)Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201819 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)BobDaveCherry88Now Bob has only the Cherry pie.How does Bob divide his asset into four equal subshares? S1 : 41 C;S2 : 41 C; S3 : 14 C; S4 : 14 CWhich subshare does Chuck choose? S4 (Or any other. They areidentical.)Now Bob has34Cherry and Dave hasRobb T. Koether (Hampden-Sydney College)The Lone-Chooser Method14Cherry.Wed, Oct 3, 201819 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)13ChuckDaveChuck has13Apple23Lemon63Apple pie and the Lemon pie.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201820 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)13ChuckDaveChuck has13Apple23Lemon63Apple pie and the Lemon pie.How does Chuck divide his assets into four equal subshares?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201820 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)13ChuckDaveChuck has13Apple23Lemon63Apple pie and the Lemon pie.How does Chuck divide his assets into four equal subshares? S1 :11113 A; S2 : 3 L; S3 : 3 L; S4 : 3 LRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201820 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)13ChuckDaveChuck has13Apple23Lemon63Apple pie and the Lemon pie.How does Chuck divide his assets into four equal subshares? S1 :11113 A; S2 : 3 L; S3 : 3 L; S4 : 3 LWhich subshare does Dave choose?Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201820 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)13ChuckDaveChuck has13Apple23Lemon63Apple pie and the Lemon pie.How does Chuck divide his assets into four equal subshares? S1 :11113 A; S2 : 3 L; S3 : 3 L; S4 : 3 LWhich subshare does Dave choose? S1Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201820 / 23

ExampleExample (The Lone-Chooser Method – 4 Players)13ChuckDaveChuck has13Apple23Lemon63Apple pie and the Lemon pie.How does Chuck divide his assets into four equal subshares? S1 :11113 A; S2 : 3 L; S3 : 3 L; S4 : 3 LWhich subshare does Dave choose? S1Now Chuck has Lemon and Dave hasRobb T. Koether (Hampden-Sydney College)The Lone-Chooser Method13Apple.Wed, Oct 3, 201820 / 23

ExampleExample (The Lone-Chooser Method – 4 06.50The final division:Andy gets 12 of the Apple pie.Bob gets 34 of the Cherry pie.Chuck gets the Lemon pie.Dave gets 12 of the Apple pie andRobb T. Koether (Hampden-Sydney College)14of the Cherry pie.The Lone-Chooser MethodWed, Oct 3, 201821 / 23

Outline1The Lone-Chooser Method2Example – 3 Players3Example – 4 Players4AssignmentRobb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201822 / 23

AssignmentAssignmentChapter 3: Exercises 41, 42.Handout exercises.Robb T. Koether (Hampden-Sydney College)The Lone-Chooser MethodWed, Oct 3, 201823 / 23

The Lone-Chooser Method Lecture 16 Section 3.4 Robb T. Koether Hampden-Sydney College Wed, Oct 3, 2018 Robb T. Koether (Hampden-Sydney College) The Lone-Chooser Method Wed, Oct 3, 2018 1

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