{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-the-strategyproofness-of-the-geometric","title":"On the Strategyproofness of the Geometric Median","arxiv_id":"2106.02394","date":"2021-06-04","proceeding":null,"authors":["El-Mahdi El-Mhamdi","Sadegh Farhadkhani","Rachid Guerraoui","Lê-Nguyên Hoang"],"abstract":"The geometric median, an instrumental component of the secure machine learning toolbox, is known to be effective when robustly aggregating models (or gradients), gathered from potentially malicious (or strategic) users. What is less known is the extent to which the geometric median incentivizes dishonest behaviors. This paper addresses this fundamental question by quantifying its strategyproofness. While we observe that the geometric median is not even approximately strategyproof, we prove that it is asymptotically $\\alpha$-strategyproof: when the number of users is large enough, a user that misbehaves can gain at most a multiplicative factor $\\alpha$, which we compute as a function of the distribution followed by the users. We then generalize our results to the case where users actually care more about specific dimensions, determining how this impacts $\\alpha$. We also show how the skewed geometric medians can be used to improve strategyproofness.","url_abs":"https://arxiv.org/abs/2106.02394v4","url_pdf":"https://arxiv.org/pdf/2106.02394v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-the-strategyproofness-of-the-geometric","repo_url":"https://github.com/sadeghfarhadkhani/gm_startegyproof","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2106.02394","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}