When Does Combining Language Models Help? A Co-Failure Ceiling on Routing, Voting, and Mixture-of-Agents Across 67 Frontier Models

No single Large Language Model (LLM) is uniformly reliable across queries, motivating multi-model inference systems that either route among models or combine their outputs. However, routing stops after selecting an initial model, while dense collaboration invokes peers on every query. We show that collaboration is non-monotonic: peers can recover failures that no model solves alone, but can also corrupt initially correct answers. We introduce COMED (Controlled Model Escalation for Multi-LLM Deliberation), a post-anchor controller for selective cross-model collaboration. COMED uses anchor self-consistency, router margin, and a lightweight peer probe to accept confident answers, verify ambiguous cases, and escalate only when collaboration is likely beneficial. We formalize this trade-off with a rescue-harm decomposition showing that selective collaboration improves when rescued errors outweigh collaboration-induced harms. Across medical, scientific, and general reasoning benchmarks, COMED improves fixed and routed anchors in all 16 open-weight settings, with gains up to +10.7 percentage points on MedQA while invoking fewer models and using fewer decoded tokens than dense collaboration. On HLE with frontier models, COMED improves GPT-5.5 from 23.1% to 28.1%, outperforming dense collaboration and achieving the best results.

Recent advances in language models have enabled collaborative settings in which multiple models leverage one another's capabilities, iteratively improving, transforming, and extending each other's outputs. Each agent sees what the others assert before it answers, so peer opinion competes with the model's own parametric knowledge, and a wrong majority can overturn an answer the model would otherwise get right. We measure that displacement in 23 open-weight models, 19 conditions, and three datasets, yielding more than a million graded responses. A unanimous wrong majority reverses 22.8% of a model's correct MMLU answers, 54.8% on GPQA and 71.0% on SimpleQA, and 84-89% of the reversed answers match the peers' answers. Existing mitigations aim to increase Resistance, the rate at which a model keeps its correct answer under this pressure, which is only half of what a collaborating agent needs. We pair it with Receptivity, the rate at which a model adopts a correct peer answer after initially answering incorrectly. We score six methods on both axes, four drawn from prior work and two of our own. Each gains Resistance only by losing Receptivity, and their means fall on a single Resistance-Receptivity frontier with $R^2$ between 0.80 and 0.90. Reflection, the strongest published method, gains 7.9 points of MMLU Resistance and gives up 15.3 of Receptivity. Reasoning is the one exception. On GPQA and SimpleQA it trades like the rest, but on the MMLU subjects whose answers a model can derive for itself it raises Resistance by 7.2 points and Receptivity by 9.6 at once, the only intervention we find that improves both.

Selecting the correct answer from a pool of candidate reasoning chains is the engine of test-time scaling, yet the standard selectors each carry a cost: self-consistency inherits the errors of the single model it resamples, and trained reward models need labeled data and transfer poorly off-distribution. We study a third signal, free at inference time: cross-model consensus, the degree to which independently trained models, each solving the problem once, agree on a final answer. We treat the panel as an LLM-jury, in which the structure of agreement, not any model's score of another, is the verification signal. Across seven benchmarks it selects correct answers better than self-consistency and far better than a model scoring its own candidates: on competition math it closes the entire gap to an oracle selector, while self-scoring closes almost none. The mechanism is error decorrelation: independently trained models err differently, so their wrong answers scatter while the correct one accumulates agreement. We make this precise with a parameter-free law, derived in closed form, that predicts consensus accuracy from three measured panel statistics to a mean absolute error of $0.03$ and exposes the method's ceiling: a shared-error floor where models share a misconception, near zero on math but non-trivial on science. Against four trained verifiers spanning discriminative, outcome, and generative reward models, the free LLM-jury matches the strongest inside their math training domain and is the top selector outside it. Cross-model consensus is thus a verifier we can characterize in advance: a law that says when to trust it, and a floor that marks where it cannot.