[Submitted on 25 Jun 2026]
[View PDF](/pdf/2606.27288)
[HTML (experimental)](https://arxiv.org/html/2606.27288v1)
Abstract:Multi-model LLM systems such as routing, voting, cascades, fusion, and mixture-of-agents are used to beat single-model accuracy. We show that their gain is capped by a quantity the field rarely reports. For any policy whose output is one member model answer, accuracy cannot exceed one minus beta, where beta is the rate at which every model is wrong on the same query. In contrast, the usual diagnostic, average pairwise error correlation rho, cannot identify beta: error laws with identical marginals and pairwise correlations can have different all-wrong rates. A Clopper-Pearson bound on beta gives a finite-sample certificate on the largest gain any router, vote, or cascade could deliver before training a router.
Across 67 models from 21 providers, a tetrachoric-calibrated single-factor model still underprices the all-wrong tail: on open-ended mathematics, observed beta is 0.052 versus 0.023 under the full 67-model Gaussian copula, about 2.5 times underpricing, with 90 percent CI 1.7 to 3.4 and k equals 17. The effect recurs on execution-graded code, where beta is 0.079. Re-asking the same GPQA-Diamond questions in free-response rather than multiple-choice form reopens the tail, with beta 0.127 and a five-judge panel with kappa 0.73 to 0.92, locating co-failure in answer format rather than subject. At matched quality, low-rho heterogeneous ensembles beat high-rho Self-MoA, but on checkable tasks in our pool, combining models rarely beats the single best model without a strong query-level routing signal. Gains come from models failing on different questions, not from adding more models.
Submission history #
From: Josef Liyanjun Chen [[view email](/show-email/e28d1956/2606.27288)]
**[v1]** Thu, 25 Jun 2026 17:06:06 UTC (230 KB)
References & Citations
...
Bibliographic Explorer
(What is the Explorer?) Connected Papers
(What is Connected Papers?) Litmaps
(What is Litmaps?) scite Smart Citations
(What are Smart Citations?)# Code, Data and Media Associated with this Article alphaXiv
(What is alphaXiv?) CatalyzeX Code Finder for Papers
(What is CatalyzeX?) DagsHub
(What is DagsHub?) Gotit.pub
(What is GotitPub?) Hugging Face
(What is Huggingface?) ScienceCast
(What is ScienceCast?)# Demos Influence Flower
(What are Influence Flowers?) CORE Recommender
(What is CORE?)# 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.