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

Rui Ai, Yuqi Pan, David Simchi-Levi, Milind Tambe, Haifeng Xu
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:1311-1340, 2026.

Abstract

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 the 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-ai26d, title = {Beyond Majority Voting: {LLM} Aggregation by Leveraging Higher-Order Information}, author = {Ai, Rui and Pan, Yuqi and Simchi-Levi, David and Tambe, Milind and Xu, Haifeng}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {1311--1340}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/ai26d/ai26d.pdf}, url = {https://proceedings.mlr.press/v306/ai26d.html}, abstract = {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 the 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.} }
Endnote
%0 Conference Paper %T Beyond Majority Voting: LLM Aggregation by Leveraging Higher-Order Information %A Rui Ai %A Yuqi Pan %A David Simchi-Levi %A Milind Tambe %A Haifeng Xu %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-ai26d %I PMLR %P 1311--1340 %U https://proceedings.mlr.press/v306/ai26d.html %V 306 %X 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 the 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.
APA
Ai, R., Pan, Y., Simchi-Levi, D., Tambe, M. & Xu, H.. (2026). Beyond Majority Voting: LLM Aggregation by Leveraging Higher-Order Information. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:1311-1340 Available from https://proceedings.mlr.press/v306/ai26d.html.

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