Better Ways to Cut a Cake - Revisited

Steven J. Brams, Michael A. Jones, Christian Klamler

    Research output: Contribution to journalConference articlepeer-review


    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 ≥ 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.

    Original languageEnglish (US)
    JournalDagstuhl Seminar Proceedings
    StatePublished - 2007
    EventFair Division 2007 - Wadern, Germany
    Duration: Jun 24 2007Jun 29 2007

    ASJC Scopus subject areas

    • Software
    • Hardware and Architecture
    • Control and Systems Engineering

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