Fair Division: Method of Lone Divider
A selected player - the Lone Divider - divides the goods into N pieces, N being the number of players. The Divider must be willing to accept any of the pieces. Other players indicate the pieces they are willing to accept.
If a piece remains unwanted by any Chooser, it is assigned to the Divider. Other pieces are put together and the division starts a new with N-1 players.
Sometimes the Choosers will indicate conflicting preferences that could be resolved, sometimes (see Richard Beigel's approach) the solution will have to be partial with subsequent new division among a smaller group of players.
Blue color in a cell means that the piece is acceptable to the player, red color means it's not. You can change a Chooser's preferences by clicking on cells in the corresponding column. After you set the Choosers' preferences, you may try to solve the problem, by assigning pieces - one at a time - to Choosers. Check the box "Solve" and keep clicking on suitable cells. If all Choosers are satisfied, the remaining pieces will be automatically assigned to the Divider.
(The number of players - in bold - could be clicked upon. To increase the number, click to the right of its vertical center line. To decrease it click to the left of the line.)
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In the simplest case where N = 2, the procedure is rather popular. One of the contestants divides the goods into two parts each of which would satisfy his idea of fairness, the other guy selects one of the two parts. This is the approach undertaking by Taran of Caer Dallbin, the Assistant Pig-Keeper [L. Alexander, Taran Wanderer, p. 81]:
"Lord Goryon shall divide the herds," Taran repeated. "But Lord Gast shall be the first to choose his half."
"Well said!" Smoit burst out, roaring with laughter. "My breath and blood, you have them there! Goryon divides and Gast chooses! Ho, oho!"
Copyright © 1996-2018 Alexander Bogomolny