Hitotsubashi Institute for Advanced Study


Fair Cake-Cutting among Families


We study the fair division of a continuous resource, such as a land-estate or 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.

Report No.: HIAS-E-79
Author(s): Erel Segal-Halevi(a)
Shmuel Nitzan(b), (c)
Affiliation: (a) Department of Computer Science, Ariel University, Ariel 40700, Israel
(b) Department of Economics, Bar Ilan University, Ramat Gan 52900, Israel
(c) Hitotsubashi Institute for Advanced Study, Hitotsubashi University
Issued Date: November 2018
Keywords: fair division, cake-cutting, public good, club good, fair-share, no-envy