Two-person pie-cutting: The fairest cuts

Julius B. Barbanel, Steven J. Brams

    Research output: Contribution to journalArticle

    Abstract

    Barbanel, Brams, and Stromquist (in 2009) asked whether there exists a twoperson moving-knife procedure that yields an envy-free, undominated, and equitable allocation of a pie. We present two procedures: One yields an envy-free, almost undominated, and almost equitable allocation, whereas the second yields an allocation with the two "almosts" removed. The latter, however, requires broadening the definition of a "procedure," which raises philosophical, as opposed to mathematical, issues. An analogous approach for cakes fails because of problems in eliciting truthful preferences.

    Original languageEnglish (US)
    Pages (from-to)25-32
    Number of pages8
    JournalCollege Mathematics Journal
    Volume42
    Issue number1
    DOIs
    StatePublished - Jan 2011

    ASJC Scopus subject areas

    • Mathematics(all)
    • Education

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