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

Listed author(s):
  • Barbanel, J. B.
  • Brams, S. J.

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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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
Handle: RePEc:cvs:starer:01-07
Contact details of provider: 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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Order Information: 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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  1. Francis Su, "undated". "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges.
  2. 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.
  3. Elisha Peterson & Francis Su, 2000. "Four-Person Envy-Free Chore Division," Claremont Colleges Working Papers 2000-48, Claremont Colleges.
  4. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446.
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