Brams, Steven J. ;
Jones, Michael A. ;
Klamler, Christian
Better Ways to Cut a Cake - Revisited
Abstract
Procedures to divide a cake among n people with n-1 cuts (the minimum number) are analyzed and compared. For 2 persons, cut-and-choose, while envy-free and efficient, limits the cutter to exactly 50% if he or she is ignorant of the chooser's preferences, whereas the chooser can generally obtain more. By comparison, a new 2-person surplus procedure (SP'), which induces the players to be truthful in order to maximize their minimum allocations, leads to a proportionally equitable division of the surplus - the part that remains after each player receives 50% - by giving each person a certain proportion of the surplus as he or she values it.
For n geq 3 persons, a new equitable procedure (EP) yields a maximally equitable division of a cake. This division gives all players the highest common value that they can achieve and induces truthfulness, but it may not be envy-free. The applicability of SP' and EP to the fair division of a heterogeneous, divisible good, like land, is briefly discussed.
BibTeX - Entry
@InProceedings{brams_et_al:DSP:2007:1227,
author = {Steven J. Brams and Michael A. Jones and Christian Klamler},
title = {Better Ways to Cut a Cake - Revisited},
booktitle = {Fair Division},
year = {2007},
editor = {Steven Brams and Kirk Pruhs and Gerhard Woeginger},
number = {07261},
series = {Dagstuhl Seminar Proceedings},
ISSN = {1862-4405},
publisher = {Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2007/1227},
annote = {Keywords: Fair division, cake-cutting, envy-freeness, strategy-proofness}
}
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Keywords: |
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Fair division, cake-cutting, envy-freeness, strategy-proofness |
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Seminar: |
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07261 - Fair Division
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Issue date: |
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2007 |
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Date of publication: |
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26.11.2007 |
