Fair Cake-Cutting among Families

TL;DR

This paper explores fair division methods for allocating continuous resources among families, considering different fairness criteria and analyzing their properties and compatibility with efficiency.

Contribution

It introduces and compares three fairness notions—average, unanimous, and democratic—for group-based resource division, analyzing their structural and efficiency aspects.

Findings

Average fairness allows for connected divisions.

Unanimous fairness is more restrictive but ensures all members agree.

Democratic fairness balances individual preferences within families.

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.