# Quantifying Diversity of Thought: A Predictive Law of Weighted LLM Ensemble Lift

arXiv: https://arxiv.org/abs/2607.17384 · HTML: https://mlsanity.com/paper/2607.17384/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 10 of its 42 references that are in the map.
- First posted on arXiv 19 Jul 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 10 of 10)

- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [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)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [Leak, Cheat, Repeat: Data Contamination and Evaluation Malpractices in Closed-Source LLMs](https://mlsanity.com/paper/2402.03927/) (2024)
- [A Unified Theory of Diversity in Ensemble Learning](https://mlsanity.com/paper/2301.03962/) (2023)
- [Diversity in Machine Learning](https://mlsanity.com/paper/1807.01477/) (2018)
- [Complementarity in Human-AI Collaboration: Concept, Sources, and Evidence](https://mlsanity.com/paper/2404.00029/) (2024)

## Built on by (most cited first, 5 of 5)

- [Are Diversity Metrics Measuring Diversity? A Capability-Controlled Audit of Majority-Vote Gain in LLM Ensembles](https://mlsanity.com/paper/2607.20768/) (2026)
- [Decorrelation Is Not Complementarity: Skill, Not Lineage, Governs Trusted-Monitor Ensembles](https://mlsanity.com/paper/2608.16190/) (2026)
- [Oracle Gaps in Reliability Coverage: Sampling Noise or Policy Specialization?](https://mlsanity.com/paper/2609.32996/) (2026)
- [RAIM: Robust Aggregation of Inexpensive Models for Hallucination Detection](https://mlsanity.com/paper/2609.39229/) (2026)
- [Where Do LLM Ensemble Gains Come From? Decomposing Candidate Value, Diversity, and Aggregation](https://mlsanity.com/paper/2610.18786/) (2026)

## Abstract (arXiv)

This paper provides an experimentally verified formal law for calculating the uplift that diversity of thought provides in Large Language Model (LLM) ensembles. From first principles, we derive an exact decomposition of LLM ensemble lift into rescue and damage masses, which yields a compact heuristic for calculating uplift. From this we extract the metrics which predict ensemble performance: an accuracy-adjusted correctness correlation, φadj, together with the accuracy gap and collective accuracy of the pair. We test the law on 767,520 inferences from ten open-weight models over two graduate-level science benchmarks, together with a novel agentic cybersecurity benchmark in which each model conducts digital-forensics investigations by multi-turn tool use in a network-isolated sandbox (23,520 graded trials including abstentions); all votes are released openly. Calibrated once on SuperGPQA at a 40:60 vote split, the heuristic predicts lift on the calibration set with Spearman's ρ=0.84 and, with its coefficients frozen, transfers to two datasets never used in calibration (ρ=0.51 on GPQA Diamond and 0.84 on the forensic tasks), whilst the measured swap mass tracks realised lift with R2≥ 0.96 throughout. Raw φ has almost no predictive power (R2≤ 0.09 throughout); the accuracy-adjusted φadj is markedly superior (R2=0.67 on SuperGPQA), and the heuristic combining these metrics is the most stable pre-pooling predictor across the three datasets.