# Multi-agent decision making: A Blackwell's informativeness approach

arXiv: https://arxiv.org/abs/2605.06028 · HTML: https://mlsanity.com/paper/2605.06028/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Social simulation and multi-agent debate, one of 16 directions in LLM agents and tool use.
- Builds on 49 of its 66 references that are in the map.
- First posted on arXiv 7 May 2026.

## Placed in

- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

## Builds on (most cited first, 30 of 49)

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- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
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- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
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- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedback](https://mlsanity.com/paper/2309.00267/) (2023)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [MedMCQA : A Large-scale Multi-Subject Multi-Choice Dataset for Medical domain Question Answering](https://mlsanity.com/paper/2203.14371/) (2022)
- [Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2003.08839/) (2020)
- [LLMs Get Lost In Multi-Turn Conversation](https://mlsanity.com/paper/2505.06120/) (2025)
- [QTRAN: Learning to Factorize with Transformation for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1905.05408/) (2019)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)

## Abstract (arXiv)

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.