Fair division of indivisible items

Steven J. Brams, Paul H. Edelman, Peter C. Fishburn

    Research output: Contribution to journalArticlepeer-review


    This paper analyzes criteria of fair division of a set of indivisible items among people whose revealed preferences are limited to rankings of the items and for whom no side payments are allowed. The criteria include refinements of Pareto optimality and envy-freeness as well as dominance-freeness, evenness of shares, and two criteria based on equally-spaced surrogate utilities, referred to as maxsum and equimax. Maxsum maximizes a measure of aggregate utility or welfare, whereas equimax lexicographically maximizes persons' utilities from smallest to largest. The paper analyzes conflicts among the criteria along with possibilities and pitfalls of achieving fair division in a variety of circumstances.

    Original languageEnglish (US)
    Pages (from-to)147-180
    Number of pages34
    JournalTheory and Decision
    Issue number2
    StatePublished - Sep 2003


    • Allocation of indivisible items
    • Envy-freeness
    • Fair division
    • Lexicographic maximin
    • Pareto optimality

    ASJC Scopus subject areas

    • General Decision Sciences
    • Developmental and Educational Psychology
    • Arts and Humanities (miscellaneous)
    • Applied Psychology
    • General Social Sciences
    • Economics, Econometrics and Finance(all)
    • Computer Science Applications


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