Decentralized Aggregation of LLM Predictions via Wagering Mechanisms
Authors: Yuhong Luo, David M. Pennock, Xintong Wang
Organizations: Rutgers University · DIMACS, Rutgers University
Abstract
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.
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.
The rapid development of large language models (LLMs) has motivated research on decision-making in multi-agent systems, where multiple agents collaborate to achieve shared objectives. Existing aggregation approaches, such as voting and debate, are largely ad-hoc and lack formal guarantees regarding the informativeness of the resulting decisions. In this paper, we provide a principled approach to analyse decisions made in the multi-LLM setting using Blackwell's informativeness framework. Within the Blackwell information-structure abstraction, we show that voting and debate induce information structures that are no more informative than the pooled private information of all agents. This result identifies Bayesian pooled posterior maximisation as an information-theoretic upper-bound decision rule under the Blackwell ordering. Motivated by this theoretical analysis, we introduce a practical method for LLM-based question-answering (QA) tasks that estimates each agent's posterior and approximates the pooled posterior using a product-of-posteriors estimator. Extensive experiments on six QA benchmarks demonstrate that our approach outperforms state-of-the-art multi-LLM debate and voting methods.
Probabilistic prediction systems often aggregate probability estimates from multiple models into a single decision. A common assumption is that if each model is individually calibrated, the aggregate prediction will also be well calibrated. We show that this assumption fails in multi-agent settings: individually calibrated predictors can become collectively miscalibrated when their predictions interact strategically, in the game-theoretic sense of Brier-optimal local response, even without deliberate coordination. This phenomenon arises naturally when agents are independently trained on overlapping data. We prove that under Brier-score-based aggregation with positively correlated beliefs, each agent's individually optimal report systematically underestimates the positive-class probability, yielding a Price of Anarchy greater than one whenever Cov(b_i, b_j) > 0. In a canonical setting (n = 5 agents, pairwise correlation = 0.5, base rate = 0.3), the empirically measured PoA in false-negative rate reaches 7.25x. In contrast, VCG-based aggregation aligns incentives by rewarding marginal contribution, achieving dominant-strategy incentive compatibility and near-optimal performance. Experiments on three real-world datasets (NSL-KDD, UNSW-NB15, Credit Card Fraud) show that VCG provides strong robustness while maintaining comparable accuracy. It performs particularly well in data-sparse and adversarial settings, and adaptive weighting further improves performance under distribution shift.