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A note on the undercut procedure

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  • Haris Aziz

Abstract

The undercut procedure was presented by Brams et al. (Soc Choice Welf 39:615–631, 2012 ) as a procedure for identifying an envy-free allocation when agents have preferences over sets of objects. We point out some shortcomings of the undercut procedure. We then simplify the undercut procedure of Brams et al. and show that it works under more general conditions where agents may express indifference between objects and they may not necessarily have responsive preferences over sets of objects. Finally, we show that the procedure works even if agents have unequal claims. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Haris Aziz, 2015. "A note on the undercut procedure," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 723-728, December.
    • Handle: RePEc:spr:sochwe:v:45:y:2015:i:4:p:723-728
    DOI: 10.1007/s00355-015-0877-4
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    References listed on IDEAS

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    1. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
    2. Steven Brams & D. Kilgour & Christian Klamler, 2012. "The undercut procedure: an algorithm for the envy-free division of indivisible items," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 615-631, July.
    3. David A. Kohler & R. Chandrasekaran, 1971. "A Class of Sequential Games," Operations Research, INFORMS, vol. 19(2), pages 270-277, April.
    4. Mongell, Susan & Roth, Alvin E, 1991. "Sorority Rush as a Two-Sided Matching Mechanism," American Economic Review, American Economic Association, vol. 81(3), pages 441-464, June.
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    Cited by:

    1. Steven J. Brams & D. Marc Kilgour & Christian Klamler, 2017. "Maximin Envy-Free Division of Indivisible Items," Group Decision and Negotiation, Springer, vol. 26(1), pages 115-131, January.
    2. Fedor Sandomirskiy & Erel Segal-Halevi, 2019. "Efficient Fair Division with Minimal Sharing," Papers 1908.01669, arXiv.org, revised Apr 2022.

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    More about this item

    Keywords

    C70; D61; D71;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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