# When LLMs Agree, Are They Right? Auditing Self-Consistency and Cross-Model Agreement as Confidence Signals

arXiv: https://arxiv.org/abs/2607.08065 · HTML: https://mlsanity.com/paper/2607.08065/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 9 Jul 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Builds on (most cited first, 12 of 12)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Large Language Models Are Not Robust Multiple Choice Selectors](https://mlsanity.com/paper/2309.03882/) (2023)
- [Iterative Causal Segmentation: Filling the Gap between Market Segmentation and Marketing Strategy](https://mlsanity.com/paper/2405.14743/) (2024)
- [Variance-Bounded Evaluation of Entity-Centric AI Systems Without Ground Truth: Theory and Measurement](https://mlsanity.com/paper/2509.22751/) (2025)
- [Designing AI-Resilient Assessments Using Interconnected Problems: A Theoretically Grounded and Empirically Validated Framework](https://mlsanity.com/paper/2512.10758/) (2025)

## Built on by (most cited first, 2 of 2)

- [Scaling Laws for Classical Machine Learning on Tabular Data: A Benchmark Study](https://mlsanity.com/paper/2607.21866/) (2026)
- [Decomposing Wrong-Consensus Agreement in LLM Self-Consistency](https://mlsanity.com/paper/2608.18795/) (2026)

## Abstract (arXiv)

LLM-as-judge (Zheng et al., 2023) is increasingly the default for evaluating AI systems in enterprise pipelines, often scaled to ensembles (Verga et al., 2024) or "mixture-of-experts" (Shazeer et al., 2017) panels of judges. These systems share a key assumption: that consistency -- agreement among judges, or among a model's own samples -- indicates correctness. We show this assumption is unreliable. Agreement is not accuracy: a model can agree with itself, and different models can agree with each other, out of shared bias, a memorized heuristic, or an option-position prior rather than truth. We ask when agreement is nonetheless a usable proxy, in a large-scale cross-runner study: 53 runners drew K=50 samples for assigned overlapping cases across comparisons of model tier, prompting, and scale on GPQA Diamond and AIME -- 265,000 samples. Using majority-correctness as the deployment label and a hierarchical runner-clustered bootstrap, agreement is a positive but weak predictor (rho 0.20-0.59, all positive under item-clustered resampling) whose usefulness is regime-dependent: best for unsaturated mid-tier models and for allocating compute, and worst -- over-confident yet no more accurate -- for the most consistent frontier model (agreement >=0.8 on 77% of GPQA case-result entries, 48% of those wrong). An exploratory cross-family check on three Claude tiers shows the same frontier over-confidence, with confident errors recurring across providers above a marginal-preserving null. Self-consistency is thus a conditional proxy for correctness, not a standalone confidence score. We publicly release the de-identified per-run rows and answer distributions.