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Toss one’s cake, and eat it too: partial divisions can improve social welfare in cake cutting

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  • Orit Arzi

    (Bar-Ilan University)

  • Yonatan Aumann

    (Bar-Ilan University)

  • Yair Dombb

    (Bar-Ilan University)

Abstract

We consider the problem of fairly dividing a heterogeneous good (a.k.a. “cake”) between a number of players with different tastes. In this setting, it is known that fairness requirements may result in a suboptimal division from the social welfare standpoint. Here we show that, in some cases, leaving some of the cake unallocated, and fairly dividing only the remainder of the cake may be socially preferable to any fair division of the entire cake. We study this phenomenon, providing asymptotically-tight bounds on the social improvement achievable by such partial divisions.

Suggested Citation

  • Orit Arzi & Yonatan Aumann & Yair Dombb, 2016. "Toss one’s cake, and eat it too: partial divisions can improve social welfare in cake cutting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 933-954, April.
    • Handle: RePEc:spr:sochwe:v:46:y:2016:i:4:d:10.1007_s00355-015-0943-y
    DOI: 10.1007/s00355-015-0943-y
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    References listed on IDEAS

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    1. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, April.
    2. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
    3. 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.
    4. Chambers, Christopher P., 2005. "Allocation rules for land division," Journal of Economic Theory, Elsevier, vol. 121(2), pages 236-258, April.
    5. Weller, Dietrich, 1985. "Fair division of a measurable space," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 5-17, February.
    6. Fabio Maccheroni & Fabio Maccheroni & Massimo Marinacci & Massimo Marinacci, 2003. "How to cut a pizza fairly: Fair division with decreasing marginal evaluations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 457-465, June.
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    Cited by:

    1. Erel Segal-Halevi & Balázs R. Sziklai, 2019. "Monotonicity and competitive equilibrium in cake-cutting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 363-401, September.

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