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Cake Division with Minimal Cuts: Envy-Free Procedures for 3 Person, 4 Persons, and Beyond

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Author Info
Barbanel, J. B.
Brams, S. J.

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Abstract

The minimal number of parallel cuts required to divide a cake into n pieces is n-1. A new 3-person procedure, requiring 2 parallel cuts, is given that produces an envy- free division, whereby each person thinks he or she receives at least a tied- for- largest piece. An extension of this procedure leads to a 4-person division, us ing 3 parallel cuts, that makes at most one player envious. Finally, a 4-person envy-free procedure is given, but it requires up to 5 parallel cuts, and some pieces may be disconnected. All these procedures improve on extant procedures by using fewer moving knives, making fewer people envious, or using fewer cuts. While the 4-person, 5-cut procedure is complex, endowing people with more information about others' preferences, or allowing them to do things beyond stopping moving knives, may yield simpler procedures for making envy- free divisions with minimal cuts, which are known always to exist

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Publisher Info
Paper provided by C.V. Starr Center for Applied Economics, New York University in its series Working Papers with number 01-07.

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Length: 38 pages
Date of creation: 2001
Date of revision:
Handle: RePEc:cvs:starer:01-07

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Postal: C.V. Starr Center, Department of Economics, New York University, 19 W. 4th Street, 6th Floor, New York, NY 10012
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Web page: http://econ.as.nyu.edu/object/econ.cvstarr.html
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Postal: C.V. Starr Center, Department of Economics, New York University, 19 W. 4th Street, 6th Floor, New York, NY 10012
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Related research
Keywords: FAIR DIVISION; CAKE CUTTING; ENVY-FREENESS; MAXIMIN;

Find related papers by JEL classification:
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Francis Su, . "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges. [Downloadable!]
  2. Elisha Peterson & Francis Su, 2000. "Four-Person Envy-Free Chore Division," Claremont Colleges Working Papers 2000-48, Claremont Colleges. [Downloadable!]
  3. Brams, Steven J. & Taylor, Alan D. & Zwicker, William S., 1995. "A Moving-Knife Solution to the Four-Person Envy-Free Cake-Division Problem," Working Papers 95-01, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  4. Steven J. Brams & D. Marc Kilgour, 2001. "Competitive Fair Division," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 418-443, April. [Downloadable!] (restricted)
    Other versions:
  5. Brams, Steven J. & Taylor, Alan D. & Zwicker, William S., 1994. "Old and NewMoving-Knife Schemes," Working Papers 94-30, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  6. Ichiishi, Tatsuro & Idzik, Adam, 1999. "Equitable allocation of divisible goods," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 389-400, December. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Antonio Nicolo' & Yan Yu, 2006. "Strategic Divide and Choose," "Marco Fanno" Working Papers 0022, Dipartimento di Scienze Economiche "Marco Fanno". [Downloadable!]
    Other versions:
  2. Barbanel, Julius B. & Brams, Steven J. & Stromquist, Walter, 2008. "Cutting a pie is not a piece of cake," MPRA Paper 12772, University Library of Munich, Germany. [Downloadable!]
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This page was last updated on 2009-10-28.

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