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Two-person cake-cutting: the optimal number of cuts

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  • Barbanel, Julius B.
  • Brams, Steven J.

Abstract

A cake is a metaphor for a heterogeneous, divisible good. When two players divide such a good, there is always a perfect division—one that is efficient (Pareto-optimal), envy-free, and equitable—which can be effected with a finite number of cuts under certain mild conditions; this is not always the case when there are more than two players (Brams, Jones, and Klamler, 2011b). We not only establish the existence of such a division but also provide an algorithm for determining where and how many cuts must be made, relating it to an algorithm, “Adjusted Winner” (Brams and Taylor, 1996, 1999), that yields a perfect division of multiple homogenous goods.

Suggested Citation

  • Barbanel, Julius B. & Brams, Steven J., 2011. "Two-person cake-cutting: the optimal number of cuts," MPRA Paper 34263, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:34263
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    File URL: https://mpra.ub.uni-muenchen.de/34263/1/MPRA_paper_34263.pdf
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    References listed on IDEAS

    as
    1. I. D. Hill, 2008. "Mathematics and Democracy: Designing Better Voting and Fair‐division Procedures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(4), pages 1032-1033, October.
    2. Barbanel, Julius B. & Brams, Steven J., 2010. "Two-person pie-cutting: The fairest cuts," MPRA Paper 22703, University Library of Munich, Germany.
    3. Barbanel,Julius B. Introduction by-Name:Taylor,Alan D., 2005. "The Geometry of Efficient Fair Division," Cambridge Books, Cambridge University Press, number 9780521842488.
    4. Nurmi, Hannu, 1996. "Fair division: From cake-cutting to dispute resolution : Steven J. Brams and Alan D. Taylor, (Cambridge University Press, Cambridge, 1995) pp. xiv + 272, US$ 54.95 (hardcover), US$ 18.95 (paper)," European Journal of Political Economy, Elsevier, vol. 12(1), pages 169-172, April.
    5. Weller, Dietrich, 1985. "Fair division of a measurable space," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 5-17, February.
    6. Barbanel, Julius B. & Brams, Steven J., 2004. "Cake division with minimal cuts: envy-free procedures for three persons, four persons, and beyond," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 251-269, November.
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    Citations

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    Cited by:

    1. Brams, Steven J. & Jones, Michael A. & Klamler, Christian, 2011. "N-Person cake-cutting: there may be no perfect division," MPRA Paper 34264, University Library of Munich, Germany.

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    More about this item

    Keywords

    Cake-cutting; fair division; envy-freeness; adjusted winner; heterogeneous good;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D30 - Microeconomics - - Distribution - - - General
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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