这篇论文告诉你为什么堆模型不一定管用——关键是所有模型一起错的概率。67个模型测下来，数学题上这个比例5.2%，代码题7.9%，比你想象的高。别盲目加模型了，先看看共失败率。
本研究分析了多模型LLM系统（路由、投票、级联、融合和混合智能体）的增益上限，发现任何策略的输出为单一模型答案时，准确率不能超过1减去所有模型在同一查询上都出错的比率beta。在67个来自21个提供商的模型上，开放式数学任务中beta为0.052，是高斯copula预测值0.023的约2.5倍（90%CI 1.7-3.4，k=17）。在代码执行任务中beta为0.079，GPQA-Diamond自由回答形式下beta升至0.127，且五名评审员的kappa为0.73-0.92。结论是增益来自模型在不同问题上犯错，而非增加模型数量。
When Does Combining Language Models Help? A Co-Failure Ceiling on Routing, Voting, and Mixture-of-Agents Across 67 Frontier Models
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.