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Fair cake-cutting among families

Author

Listed:
  • Erel Segal-Halevi

    (Ariel University)

  • Shmuel Nitzan

    (Bar Ilan University
    Hitotsubashi University)

Abstract

We study the fair division of a continuous resource, such as a land-estate or a time-interval, among pre-specified groups of agents, such as families. Each family is given a piece of the resource and this piece is used simultaneously by all family members, while different members may have different value functions. Three ways to assess the fairness of such a division are examined. (a) Average Fairness means that each family’s share is fair according to the “family value function”, defined as the arithmetic mean of the value functions of the family members. (b) Unanimous Fairness means that all members in all families feel that their family’s share is fair according to their personal value function. (c) Democratic Fairness means that in each family, at least a fixed fraction (e.g. a half) of the members feel that their family’s share is fair. We compare these criteria based on the number of connected components in the resulting division and on their compatibility with Pareto-efficiency.

Suggested Citation

  • Erel Segal-Halevi & Shmuel Nitzan, 2019. "Fair cake-cutting among families," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 709-740, December.
    • Handle: RePEc:spr:sochwe:v:53:y:2019:i:4:d:10.1007_s00355-019-01210-9
    DOI: 10.1007/s00355-019-01210-9
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    Cited by:

    1. Erel Segal-Halevi & Warut Suksompong, 2023. "Cutting a Cake Fairly for Groups Revisited," Papers 2301.09061, arXiv.org.
    2. Josué Ortega & Erel Segal-Halevi, 2022. "Obvious manipulations in cake-cutting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 969-988, November.
    3. Erel Segal-Halevi & Warut Suksompong, 2020. "How to Cut a Cake Fairly: A Generalization to Groups," Papers 2001.03327, arXiv.org, revised Apr 2020.
    4. Uriel Feige & Yehonatan Tahan, 2022. "On allocations that give intersecting groups their fair share," Papers 2204.06820, arXiv.org.

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