Where Do LLM Ensemble Gains Come From? Decomposing Candidate Value, Diversity, and Aggregation

LLM-as-a-judge ensembles are the standard paradigm for scalable evaluation, but their aggregation mechanisms suffer from a fundamental flaw: they implicitly assume that judges provide independent estimates of true quality. However, in practice, LLM judges exhibit correlated errors caused by shared latent confounders -- such as verbosity, stylistic preferences, or training artifacts -- causing standard aggregation rules like majority vote or averaging to provide little gain or even amplify systematic mistakes. To address this, we introduce CARE, a confounder-aware aggregation framework that explicitly models LLM judge scores as arising from both a latent true-quality signal and shared confounding factors. Rather than heuristically re-weighting judges, CARE separates quality from confounders without access to ground-truth labels. We provide theoretical guarantees for identifiability and finite-sample recovery under shared confounders, and we quantify the systematic bias incurred when aggregation models omit confounding latent factors. Across 12 public benchmarks spanning continuous scoring, binary classification, and pairwise preference settings, CARE improves aggregation accuracy, reducing error by up to 26.8%. Code is released in https://github.com/SprocketLab/CARE.

Multi-AI collaboration, such as ensembling or debating large language models (LLMs), is a promising paradigm for aggregating information and boosting performance. A foundational step in these pipelines is to feed the responses of several proposer LLMs into a summarizer LLM, which synthesizes a better answer. However, choosing which proposers to include is non-trivial. Existing approaches primarily focus either on accuracy (picking the strongest models) or diversity (ensuring variety), and often overlook the interactions among proposers and with the summarizer. We reframe proposer selection as a combinatorial selection problem akin to feature selection, where the value of an LLM lies in its complementarity with others. However, directly applying standard feature-selection algorithms is impractical in the LLM setting due to prohibitive time complexity. Motivated by this limitation, we explore an extensive range of computationally feasible, greedy-style selection algorithms that assess complementarity using a small labeled set. Our experiments validate complementarity as a guiding principle for proposer selection and identify methods that achieve the best performance-cost trade-offs in practice.

Majority voting over LLMs is widely assumed to benefit from diversity, and diversity measures are used to choose which models to combine. We ask whether five such measures track diversity or mainly re-express capability, auditing them as predictors of majority-vote gain over the best member across 31,900 subsets of 30 LLMs on MMLU-Pro (29 on TruthfulQA) under explicit capability controls. Three findings emerge. First, latent complementarity is ubiquitous: oracle gain is positive in 100% of subsets, yet simple voting beats the strongest member in only 9.98% of all canonical size-3 subsets (18.71% with held-out best selection); the pooled size-2-4 rate is 1.27%, partly reflecting deterministic even-size voting behavior. Second, a joint-correctness proxy (strict diversity) is nearly collinear with one minus mean accuracy (size-3 Spearman rho = +0.991 / +0.988); raw diversity-gain associations are strongly capability-entangled and, with one exception, unstable under control. Third, three linear contingency-table statistics are algebraically non-separable; after capability control, the empirically stable remainder is a modest residual pairwise co-failure association in which more shared error corresponds to lower gain. This direction is robust, but its magnitude is configuration-dependent. Joint rawspace linear regressions treating strict diversity, disagreement, and double-fault as independent predictors are rank-deficient by construction.