# Proportional Fairness in Obnoxious Facility Location

arXiv: https://arxiv.org/abs/2301.04340 · HTML: https://mlsanity.com/paper/2301.04340/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 45 references that are in the map.
- First posted on arXiv 11 Jan 2023.

## Builds on (most cited first, 9 of 9)

- [Mechanism Design for Facility Location Problems: A Survey](https://mlsanity.com/paper/2106.03457/) (2021)
- [Fair mixing: the case of dichotomous preferences](https://mlsanity.com/paper/1712.02542/) (2017)
- [The Price of Fairness for Indivisible Goods](https://mlsanity.com/paper/1905.04910/) (2019)
- [Strategyproof and Proportionally Fair Facility Location](https://mlsanity.com/paper/2111.01566/) (2021)
- [Two-Stage Facility Location Games with Strategic Clients and Facilities](https://mlsanity.com/paper/2105.01425/) (2021)
- [Strategyproof Mechanisms For Group-Fair Facility Location Problems](https://mlsanity.com/paper/2107.05175/) (2021)
- [Strategyproof Mechanisms for One-Dimensional Hybrid and Obnoxious Facility Location](https://mlsanity.com/paper/1412.3414/) (2014)
- [Random Rank: The One and Only Strategyproof and Proportionally Fair Randomized Facility Location Mechanism](https://mlsanity.com/paper/2205.14798/) (2022)
- [A Probabilistic Approach to Voting, Allocation, Matching, and Coalition Formation](https://mlsanity.com/paper/2002.10171/) (2020)

## Built on by (most cited first, 3 of 3)

- [Proportional Selection in Networks](https://mlsanity.com/paper/2502.03545/) (2025)
- [Equitable Mechanism Design for Facility Location](https://mlsanity.com/paper/2506.10460/) (2025)
- [Prediction-Augmented Mechanism Design for Weighted Facility Location](https://mlsanity.com/paper/2507.06509/) (2025)

## Abstract (arXiv)

We consider the obnoxious facility location problem (in which agents prefer the facility location to be far from them) and propose a hierarchy of distance-based proportional fairness concepts for the problem. These fairness axioms ensure that groups of agents at the same location are guaranteed to be a distance from the facility proportional to their group size. We consider deterministic and randomized mechanisms, and compute tight bounds on the price of proportional fairness. In the deterministic setting, we show that our proportional fairness axioms are incompatible with strategyproofness, and prove asymptotically tight ε-price of anarchy and stability bounds for proportionally fair welfare-optimal mechanisms. In the randomized setting, we identify proportionally fair and strategyproof mechanisms that give an expected welfare within a constant factor of the optimal welfare. Finally, we prove existence results for two extensions to our model.