Cake division with minimal cuts: Envy-free procedures for three persons, four persons, and beyond

Julius B. Barbanel, Steven J. Brams

    Research output: Contribution to journalArticlepeer-review

    Abstract

    The minimal number of parallel cuts required to divide a cake into n pieces is n-1. A new 3-person procedure, requiring two 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, using three parallel cuts, which makes at most one person envious. Finally, a 4-person envy-free procedure is given, but it requires up to five 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.

    Original languageEnglish (US)
    Pages (from-to)251-269
    Number of pages19
    JournalMathematical social sciences
    Volume48
    Issue number3
    DOIs
    StatePublished - Nov 2004

    Keywords

    • Cake-cutting
    • Envy-freeness
    • Fair division
    • Minimal cuts
    • Moving-knife algorithm

    ASJC Scopus subject areas

    • Sociology and Political Science
    • Social Sciences(all)
    • Psychology(all)
    • Statistics, Probability and Uncertainty

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