テクニカルレポート Fair Cake-Cutting among Families

SEGAL-HALEVI, Erel  ,  NITZAN, Shmuel

2018-11 , Hitotsubashi Institute for Advanced Study, Hitotsubashi University
内容記述
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 received a fair share according to their personal value function. (c) *Democratic fairness* means that in each family, at least half 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 based on their compatibility with Pareto-efficiency.
This research was funded in part by the following institutions: The Doctoral Fellowships of Excellence Program at Bar-Ilan University, the Mordechai and Monique Katz Graduate Fellowship Program, and the Israel Science Foundation grant 1083/13.
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http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/29686/1/070_hiasDP-E-79.pdf

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