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[Submitted on 13 Oct 2026] Title:Similar Models, Broken Odds: Where Luce's Axiom Fails in Chatbot Arena View a PDF of the paper titled Similar Models, Broken Odds: Where Luce's Axiom Fails in Chatbot Arena, by Soovadeep Bakshi and 3 other authors View PDF HTML (experimental) Abstract:Chatbot Arena ranks language models with the Bradley-Terry model, which gives each model one score and so assumes Luce's choice axiom. Choice theory predicts where this fails: near-copies are told apart more decisively than their scores imply. On 1.8 million Arena votes, votes between versions of one model are 1.37 times as decisive as Bradley-Terry predicts, between sizes of one generation 1.26 times and between models of one lab 1.12 times; a release a year later gives consistent multipliers, and the effect survives alternative tie treatments, prompt subsets and topics, and timing checks. How alike two models' answers are worded and formatted tracks the effect. A correction with four to six parameters predicts held-out votes better than Bradley-Terry and than models with hundreds of parameters, mostly by modelling ties; frozen and carried to new releases in a test fixed in advance, its gains are concentrated in ties, and better head-to-head odds are not established. The leaderboard order barely moves. With language-model judges and three-answer menus, a near-copy takes votes mostly from its twin when choices are pooled over prompts (log-odds shift +0.10, 95% interval 0.05 to 0.16); within a prompt the shift is smaller and clear for two of four judges. Comments: 18 pages, 5 figures, 9 tables Subjects: Computation and Language (cs.CL); Machine Learning (cs.LG) Cite as: arXiv:2610.19095 [cs.CL] (or arXiv:2610.19095v1 [cs.CL] for this version) https://doi.org/10.48550/arXiv.2610.19095 arXiv-issued DOI via DataCite (pending registration) Submission history From: Soovadeep Bakshi [view email] [v1] Tue, 13 Oct 2026 19:33:25 UTC (170 KB) Full-text links: Access Paper: View a PDF of the paper titled Similar Models, Broken Odds: Where Luce's Axiom Fails in Chatbot Arena, by Soovadeep Bakshi and 3 other authors View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.CL new | recent | 2026-10 Change to browse by: cs cs.LG References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)