# Weighted Fairness Notions for Indivisible Items Revisited

arXiv: https://arxiv.org/abs/2112.04166 · HTML: https://mlsanity.com/paper/2112.04166/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2021.

## Built on by (most cited first, 4 of 4)

- [Online Fair Division with Additional Information](https://mlsanity.com/paper/2505.24503/) (2025)
- [Fairness in Forecasting of Observations of Linear Dynamical Systems](https://mlsanity.com/paper/2209.05274/) (2022)
- [Fair Allocation in Dynamic Mechanism Design](https://mlsanity.com/paper/2406.00147/) (2024)
- [Multilevel Fair Allocation under Additive Preferences](https://mlsanity.com/paper/2608.24400/) (2026)

## Abstract (arXiv)

We revisit the setting of fairly allocating indivisible items when agents have different weights representing their entitlements. First, we propose a parameterized family of relaxations for weighted envy-freeness and the same for weighted proportionality; the parameters indicate whether smaller-weight or larger-weight agents should be given a higher priority. We show that each notion in these families can always be satisfied, but any two cannot necessarily be fulfilled simultaneously. We then introduce an intuitive weighted generalization of maximin share fairness and establish the optimal approximation of it that can be guaranteed. Furthermore, we characterize the implication relations between the various weighted fairness notions introduced in this and prior work, and relate them to the lower and upper quota axioms from apportionment.