Fair cake-cutting among families

Abstract

We study the fair division of a continuous resource, such as a landestate 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.

Incentives against Max‐Min Fairness in a Centralized Resource System

“…How to help players achieve fair allocations is one of the most important strands in cakecutting problem. Since then, a large number of related studies have emerged [5,19,20].…”

Group Envy Freeness and Group Pareto Efficiency in Fair Division with Indivisible Items

“…More group fairness notions have been studied in the context of cake-cutting (e.g. arithmetic-mean-proportionality, geometric-mean-proportionality, minimum-proportionality, median-proportionality) [33]. These notions compare the aggregate bundle of each group of agents to their proportional (wrt the number of groups) aggregate bundle of all items.…”

“…We thus assume that each group has some aggregate utility for a given bundle of items of another group. As in [33], we consider arithmetic-mean group utilities. We study this problem for five main reasons.…”

Almost Envy-Freeness for Groups: Improved Bounds via Discrepancy Theory

“…The group aspect of fair division has been addressed in a number of papers in the past few years [Manurangsi and Suksompong, 2017;Ghodsi et al, 2018;Suksompong, 2018;Segal-Halevi and Nitzan, 2019;Segal-Halevi and Suksompong, 2019;Kyropoulou et al, 2020;Segal-Halevi and Suksompong, 2021]. Most of these papers studied the important fairness notion of envy-freeness: an agent is said to be envy-free if she values the goods allocated to her group at least as much as those allocated to any other group.…”