Divide-and-conquer: A proportional, minimal-envy cake-cutting algorithm

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

    Research output: Contribution to journalArticle

    Abstract

    We analyze a class of proportional cake-cutting algorithms that use a minimal number of cuts (n - 1 if there are n players) to divide a cake that the players value along one dimension. While these algorithms may not produce an envy-free or efficient allocation-as these terms are used in the fair-division literature-one, divide-and-conquer (D&C), minimizes the maximum number of players that any single player can envy. It works by asking n ≥ 2 players successively to place marks on a cake-valued along a line-that divide it into equal halves (when n is even) or nearly equal halves (when n is odd), then halves of these halves, and so on. Among other properties, D&C ensures players of at least 1/n shares, as they each value the cake, if and only if they are truthful. However, D&C may not allow players to obtain proportional, connected pieces if they have unequal entitlements. Possible applications of D&C to land division are briefly discussed.

    Original languageEnglish (US)
    Pages (from-to)291-307
    Number of pages17
    JournalSIAM Review
    Volume53
    Issue number2
    DOIs
    StatePublished - 2011

    Keywords

    • Binary tree
    • Cake-cutting
    • Fair division
    • Minimal envy
    • Proportional algorithm

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computational Mathematics
    • Applied Mathematics

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