Weighted Envy-Freeness Revisited: Indivisible Resource and House Allocations

TL;DR

This paper revisits weighted envy-freeness in resource and house allocations, proposing a new fairness concept that improves the existence of fair solutions and analyzing their computational complexity.

Contribution

It introduces SumAvg-envy-freeness, a new fairness concept that enhances the feasibility of fair allocations, and studies its computational complexity in classic allocation problems.

Findings

SumAvg-envy-freeness increases the existence of fair allocations.

The paper characterizes properties of weighted envy-freeness.

Complexity results are provided for finding fair allocations under new and old concepts.

Abstract

Envy-Freeness is one of the most fundamental and important concepts in fair allocation. Some recent studies have focused on the concept of weighted envy-freeness. Under this concept, each agent is assigned a weight, and their valuations are divided by their weights when assessing fairness. This concept can promote more fairness in some scenarios. But on the other hand, experimental research has shown that this weighted envy-freeness significantly reduces the likelihood of fair allocations. When we must allocate the resources, we may propose fairness concepts with lower requirements that are potentially more feasible to implement. In this paper, we revisit weighted envy-freeness and propose a new concept called SumAvg-envy-freeness, which substantially increases the existence of fair allocations. This new concept can be seen as a complement of the normal weighted envy-fairness. Furthermore, we systematically study the computational complexity of finding fair allocations under the old and new weighted fairness concepts in two types of classic problems: Indivisible Resource Allocation and House Allocation. Our study provides a comprehensive characterization of various properties of weighted envy-freeness.