# Decentralized Aggregation of LLM Predictions via Wagering Mechanisms

arXiv: https://arxiv.org/abs/2607.04389 · HTML: https://mlsanity.com/paper/2607.04389/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 47 of its 63 references that are in the map.
- First posted on arXiv 5 Jul 2026.

## Builds on (most cited first, 30 of 47)

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- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [DeBERTaV3: Improving DeBERTa using ELECTRA-Style Pre-Training with Gradient-Disentangled Embedding Sharing](https://mlsanity.com/paper/2111.09543/) (2021)
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- [Approaching Human-Level Forecasting with Language Models](https://mlsanity.com/paper/2402.18563/) (2024)
- [RouterDC: Query-Based Router by Dual Contrastive Learning for Assembling Large Language Models](https://mlsanity.com/paper/2409.19886/) (2024)
- [Harnessing Multiple Large Language Models: A Survey on LLM Ensemble](https://mlsanity.com/paper/2502.18036/) (2025)
- [Debate or Vote: Which Yields Better Decisions in Multi-Agent Large Language Models?](https://mlsanity.com/paper/2508.17536/) (2025)
- [Wisdom of the Silicon Crowd: LLM Ensemble Prediction Capabilities Rival Human Crowd Accuracy](https://mlsanity.com/paper/2402.19379/) (2024)
- [Forecasting Future World Events with Neural Networks](https://mlsanity.com/paper/2206.15474/) (2022)
- [FutureX: An Advanced Live Benchmark for LLM Agents in Future Prediction](https://mlsanity.com/paper/2508.11987/) (2025)
- [Calibrating Language Models with Adaptive Temperature Scaling](https://mlsanity.com/paper/2409.19817/) (2024)
- [Pack of LLMs: Model Fusion at Test-Time via Perplexity Optimization](https://mlsanity.com/paper/2404.11531/) (2024)

## Abstract (arXiv)

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.