{"type":"ScholarlyArticle","title":"Equitable Mechanism Design for Facility Location","authors":[{"name":"Toby Walsh","slug":"toby-walsh","given":"Toby","family":"Walsh","affiliation":""}],"abstract":"We consider strategy proof mechanisms for facility location which maximize equitability between agents. As is common in the literature, we measure equitability with the Gini index. We first prove a simple but fundamental impossibility result that no strategy proof mechanism can bound the approximation ratio of the optimal Gini index of utilities for one or more facilities. We propose instead computing approximation ratios of the complemented Gini index of utilities, and consider how well both deterministic and randomized mechanisms approximate this. In addition, as Nash welfare is often put forwards as an equitable compromise between egalitarain and utilitarian outcomes, we consider how well mechanisms approximate the Nash welfare.","doi":"10.24963/ijcai.2025/32","url":"https://ijcai.org/proceedings/2025/32","pdf":"https://ijcai.org/proceedings/2025/0032.pdf","markdown":"https://ijcai.org/proceedings/2025/32.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/32","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":32,"pages":{"first":275,"last":283},"keywords":["Agent-based and Multi-agent Systems: MAS: Resource allocation","Agent-based and Multi-agent Systems: MAS: Agent theories and models","Agent-based and Multi-agent Systems: MAS: Applications","Agent-based and Multi-agent Systems: General"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}