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Why Chatbot Arena Understates "New Version Beats Old": Luce's Axiom, Sibling Models, and Bradley–Terry Bias
A close read of arXiv:2610.19095. Chatbot Arena (LMArena) gives each model one Bradley–Terry score, which assumes Luce's choice axiom. On 1.8 million votes, versions of one model are judged 1.37x more decisively than their score gap implies, sizes of one generation 1.26x, models of one lab 1.12x. The overall order barely moves, but head-to-head odds between siblings are pulled toward even. The mechanism, how strong each piece of evidence is, how it relates to style control and the Leaderboard Illusion, and what to do when you read or build a pairwise leaderboard.
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