# Strategyproof Mechanisms For Group-Fair Facility Location Problems

arXiv: https://arxiv.org/abs/2107.05175 · HTML: https://mlsanity.com/paper/2107.05175/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2021.

## Built on by (most cited first, 5 of 5)

- [Strategyproof and Proportionally Fair Facility Location](https://mlsanity.com/paper/2111.01566/) (2021)
- [Random Rank: The One and Only Strategyproof and Proportionally Fair Randomized Facility Location Mechanism](https://mlsanity.com/paper/2205.14798/) (2022)
- [Proportional Fairness in Obnoxious Facility Location](https://mlsanity.com/paper/2301.04340/) (2023)
- [Proportional Selection in Networks](https://mlsanity.com/paper/2502.03545/) (2025)
- [Facility Location Games Beyond Single-Peakedness: the Entrance Fee Model](https://mlsanity.com/paper/2204.11282/) (2022)

## Abstract (arXiv)

We study the facility location problems where agents are located on a real line and divided into groups based on criteria such as ethnicity or age. Our aim is to design mechanisms to locate a facility to approximately minimize the costs of groups of agents to the facility fairly while eliciting the agents' locations truthfully. We first explore various well-motivated group fairness cost objectives for the problems and show that many natural objectives have an unbounded approximation ratio. We then consider minimizing the maximum total group cost and minimizing the average group cost objectives. For these objectives, we show that existing classical mechanisms (e.g., median) and new group-based mechanisms provide bounded approximation ratios, where the group-based mechanisms can achieve better ratios. We also provide lower bounds for both objectives. To measure fairness between groups and within each group, we study a new notion of intergroup and intragroup fairness (IIF) . We consider two IIF objectives and provide mechanisms with tight approximation ratios.