Multi-stakeholder tasks require one output to satisfy users with conflicting preferences. Holistic LLM judges conflate utility estimation and utility aggregation, yielding unstable implicit weights. We show empirically and theoretically that this aggregation-specific \emph{weighting noise} can create large score shifts when stakeholder satisfaction is dispersed; in our experiments, these weight-induced shifts also increase with stakeholder count. We propose \textsc{DecompR}: counterfactual-calibrated weights are fixed from query structure before candidate scoring, while per-role utilities are estimated independently, removing candidate-dependent weight drift and reducing estimation noise.
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 \href{https://github.com/SprocketLab/CARE}{https://github.com/SprocketLab/CARE}.
Multi-Agent Debate (MAD) has been widely adopted to improve LLM-based evaluation by prompting multiple agents to negotiate and reach a consensus. However, for subjective rubric-based scoring, inter-agent agreement does not guarantee alignment with human judgments. In this paper, we compare a single-judge baseline against a consensus-based MAD protocol on subjective evaluation tasks and design three ablations to isolate the impact of role prompting, multi-round interaction, and explicit score sharing. Evaluations across six LLMs show that the single-judge baseline achieves the strongest human alignment on average across six judge models, whereas MAD shows degradation in human alignment on both tasks. Our ablations demonstrate that this performance drop stems primarily from asymmetric role prompting rather than the interaction itself. Specifically, assigning a strict judge role introduces a systematic downward bias that the consensus process fails to correct. The central finding is that this bias reflects strict-stance dominance beyond averaging: the consensus score falls well beyond the arithmetic midpoint of the standalone strict and lenient conditions, rather than averaging them out. Removing role asymmetry (Symmetric MAD) largely recovers baseline performance, while masking peer scores widens inter-agent disagreement on average and worsens average human alignment. These findings demonstrate that multi-agent consensus can enforce artificial agreement at the expense of true human alignment, revealing a structural limitation in consensus-style, role-specialized MAD protocols for subjective scoring.
It is increasingly common to aggregate predictions from multiple LLMs, each with domain expertise or access to private tools and data, to improve collective prediction performance. In decentralized settings, aggregation weights need to be determined without access to models' private information and should remain robust to strategic reporting. We propose a family of advantage-aligned wagering mechanisms for LLM aggregation (WALLA), in which each model reports a prediction and a learned wager, and predictions are aggregated using wagers as weights. WALLA introduces a leave-one-out baseline into the net payout function, yielding three desirable properties: (1) dominant-strategy incentive compatibility of prediction under arbitrary belief structure, (2) advantage--wager alignment, where the optimal wager is proportional to the model's expected score advantage, and (3) prediction-agnostic wager optimization, enabling decentralized learning of wager policies without requiring optimal predictions. We further instantiate two mechanism variants that trade off normality and no-arbitrage while maintaining a bounded worst-case deficit for the mechanism. Experiments on question-answering and forecasting benchmarks across heterogeneous models and private-information settings show that WALLA matches centralized aggregation methods in predictive performance, while simultaneously achieving decentralized learning, advantage-aligned aggregation weights, uncertainty awareness, and incentive-compatible prediction.