# Beyond Majority Voting: LLM Aggregation by Leveraging Higher-Order Information

arXiv: https://arxiv.org/abs/2510.01499 · HTML: https://mlsanity.com/paper/2510.01499/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 44 of its 68 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- 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 44)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)
- [Debating with More Persuasive LLMs Leads to More Truthful Answers](https://mlsanity.com/paper/2402.06782/) (2024)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [ForecastBench: A Dynamic Benchmark of AI Forecasting Capabilities](https://mlsanity.com/paper/2409.19839/) (2024)
- [Multiagent Finetuning: Self Improvement with Diverse Reasoning Chains](https://mlsanity.com/paper/2501.05707/) (2025)
- [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)
- [Merge, Ensemble, and Cooperate! A Survey on Collaborative Strategies in the Era of Large Language Models](https://mlsanity.com/paper/2407.06089/) (2024)
- [Field Study in Deploying Restless Multi-Armed Bandits: Assisting Non-Profits in Improving Maternal and Child Health](https://mlsanity.com/paper/2109.08075/) (2021)
- [LLM-TOPLA: Efficient LLM Ensemble by Maximising Diversity](https://mlsanity.com/paper/2410.03953/) (2024)
- [LLM-Ensemble: Optimal Large Language Model Ensemble Method for E-commerce Product Attribute Value Extraction](https://mlsanity.com/paper/2403.00863/) (2024)
- [Serial Position Effects of Large Language Models](https://mlsanity.com/paper/2406.15981/) (2024)
- [A Comparative Study on Annotation Quality of Crowdsourcing and LLM via Label Aggregation](https://mlsanity.com/paper/2401.09760/) (2024)

## Built on by (most cited first, 26 of 26)

- [Don't Always Pick the Highest-Performing Model: An Information Theoretic View of LLM Ensemble Selection](https://mlsanity.com/paper/2602.08003/) (2026)
- [Are Diversity Metrics Measuring Diversity? A Capability-Controlled Audit of Majority-Vote Gain in LLM Ensembles](https://mlsanity.com/paper/2607.20768/) (2026)
- [Epistemic Gain, Aleatoric Cost: Uncertainty Decomposition in Multi-Agent Debate for Math Reasoning](https://mlsanity.com/paper/2603.01221/) (2026)
- [Minority Sentinel: When to Overturn Majority Voting in Multi-Agent LLM Debates](https://mlsanity.com/paper/2606.29270/) (2026)
- [Unifying Temporal and Structural Credit Assignment in LLM-Based Multi-Agent Prompt Optimization](https://mlsanity.com/paper/2605.30227/) (2026)
- [RAL2M: Retrieval Augmented Learning-To-Match Against Hallucination in Compliance-Guaranteed Service Systems](https://mlsanity.com/paper/2601.02917/) (2026)
- [Dependence-Aware Label Aggregation for LLM-as-a-Judge via Ising Models](https://mlsanity.com/paper/2601.22336/) (2026)
- [Multi-LLM Query Optimization](https://mlsanity.com/paper/2603.24617/) (2026)
- [Prior-Agnostic Robust Forecast Aggregation](https://mlsanity.com/paper/2604.24517/) (2026)
- [When Does Delegation Beat Majority? A Delegation-Based Aggregator for Multi-Sample LLM Inference](https://mlsanity.com/paper/2606.08098/) (2026)
- [Robust Persona-Aware Toxicity Detection with Prompt Optimization and Learned Ensembling](https://mlsanity.com/paper/2601.02337/) (2026)
- [SCoOP: Semantic Consistent Opinion Pooling for Uncertainty Quantification in Multiple Vision-Language Model Systems](https://mlsanity.com/paper/2603.23853/) (2026)
- [Multi-agent decision making: A Blackwell's informativeness approach](https://mlsanity.com/paper/2605.06028/) (2026)
- [Efficient Ensemble Selection from Binary and Pairwise Feedback](https://mlsanity.com/paper/2605.09588/) (2026)
- [Certifiable Semantic Agreement Among LLM Agents: What the Admissibility Instrument Decides](https://mlsanity.com/paper/2606.07316/) (2026)
- [Uncertainty-Aware Trust Estimation for Multi-LLM Systems via Structured Expert Judgement](https://mlsanity.com/paper/2607.20529/) (2026)
- [Evaluating Large Language Models for Symbolic Security Protocol Analysis](https://mlsanity.com/paper/2607.20712/) (2026)
- [Test-Time Augmentation for LLMs: When Input Diversity Beats Output Diversity at Matched Compute](https://mlsanity.com/paper/2608.09351/) (2026)
- [Divergent-Convergent Reasoning: Scaling Test-Time Compute through Structured Solution Synthesis](https://mlsanity.com/paper/2608.15303/) (2026)
- [Diverse by Reasoning: Harnessing the Wisdom of LLM Crowds for Future Prediction](https://mlsanity.com/paper/2608.24001/) (2026)
- [Performance Foundations of Parallel & Distributed Reasoning Language Models](https://mlsanity.com/paper/2608.27046/) (2026)
- [CUSP: Decomposable Collective Uncertainty for Multi-Agent Multimodal Reasoning](https://mlsanity.com/paper/2609.05708/) (2026)
- [When Agents Disagree: Bayesian Backward Reasoning as a Label-Free Anchor for Multi-Agent Collective Decision-Making](https://mlsanity.com/paper/2609.11709/) (2026)
- [Count Evidence, Not Sentences: Tempered Evidence Fusion of LLM Judgments for Long-Text Value Measurement](https://mlsanity.com/paper/2609.27165/) (2026)
- [Social Circuits behind Multi-agent Echo Chambers](https://mlsanity.com/paper/2609.34444/) (2026)
- [Refinement as a Service: Algorithmic Predictor Refinement](https://mlsanity.com/paper/2610.11415/) (2026)

## Abstract (arXiv)

With the rapid progress of multi-agent large language model (LLM) reasoning, how to effectively aggregate answers from multiple LLMs has emerged as a fundamental challenge. Standard majority voting treats all answers equally, failing to consider latent heterogeneity and correlation across models. In this work, we design two new aggregation algorithms called Optimal Weight (OW) and Inverse Surprising Popularity (ISP), leveraging both first-order and second-order information. Our theoretical analysis shows these methods provably mitigate inherent limitations of majority voting under mild assumptions, leading to more reliable collective decisions. We empirically validate our algorithms on synthetic datasets, popular LLM fine-tuning benchmarks such as UltraFeedback and MMLU, and a real-world healthcare setting ARMMAN. Our algorithms consistently outperform standard baselines, establishing a robust, training-free framework for effective multi-agent LLM aggregation.