# Decomposing Wrong-Consensus Agreement in LLM Self-Consistency

arXiv: https://arxiv.org/abs/2608.18795 · HTML: https://mlsanity.com/paper/2608.18795/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 28 references that are in the map.
- First posted on arXiv 19 Aug 2026.

## Builds on (most cited first, 15 of 15)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Correlated Errors in Large Language Models](https://mlsanity.com/paper/2506.07962/) (2025)
- [Beyond Semantic Entropy: Boosting LLM Uncertainty Quantification with Pairwise Semantic Similarity](https://mlsanity.com/paper/2506.00245/) (2025)
- [Too Consistent to Detect: A Study of Self-Consistent Errors in LLMs](https://mlsanity.com/paper/2505.17656/) (2025)
- [Certified Self-Consistency: Statistical Guarantees and Test-Time Training for Reliable Reasoning in LLMs](https://mlsanity.com/paper/2510.17472/) (2025)
- [Complementing Self-Consistency with Cross-Model Disagreement for Uncertainty Quantification](https://mlsanity.com/paper/2604.17112/) (2026)
- [Are Diversity Metrics Measuring Diversity? A Capability-Controlled Audit of Majority-Vote Gain in LLM Ensembles](https://mlsanity.com/paper/2607.20768/) (2026)
- [The Consistency Hypothesis in Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2506.21849/) (2025)
- [Beyond Consensus: Trace-Level Synthesis in Mixture of Agents](https://mlsanity.com/paper/2605.29116/) (2026)
- [When Self-Consistency Backfires: Majority Vote Hurts the Majority of Hard Science Problems for Small LLMs](https://mlsanity.com/paper/2608.11403/) (2026)
- [When LLMs Agree, Are They Right? Auditing Self-Consistency and Cross-Model Agreement as Confidence Signals](https://mlsanity.com/paper/2607.08065/) (2026)
- [Stochastic Sampling is Epistemically Shallow: The Dimensionality Gap Between Temperature Variation and Model Diversity in LLMs](https://mlsanity.com/paper/2607.20464/) (2026)
- [AnchorScore: A CLIP-Based Diagnostic of MLLM Annotation Difficulty](https://mlsanity.com/paper/2608.16690/) (2026)

## Abstract (arXiv)

Agreement among repeated samples of a language model is routinely read as evidence about answer reliability, yet wrong answers can agree just as strongly as right ones. This paper asks what information wrong-consensus agreement actually contains, and answers with a quantitative decomposition. A pluralistic agreement index Gamma, normalized by the reference scale d=(1-p)/(C-1), is split into a mechanical component (agreement delivered by a per-case answer preference alone) and a preference-unexplained residual. The mechanical reference is leak-free: each case's preference and accuracy are estimated from its other runs only. On public GPT-4.1 per-run data, coverage phi (the mechanical/empirical ratio) shows a benchmark-associated direction: 0.81-0.93 on multiple-choice GPQA-Diamond against 0.59-0.78 on open-domain AIME, where a residual of 1.54-2.80 Gamma units survives, more than absorbed by a calibrated run-level preference-heterogeneity reference. A controlled replication under one fixed protocol (four runs per question, K=32 votes) on five open-weights checkpoints (Qwen3.5-9B/122B, Qwen3.8-27B, Gemma4-26B/31B) finds near-complete mechanical coverage in all ten cells (phi approximately 1, with a small overshoot consistent with a quantified finite-donor plug-in bias), robust to a two-run design; the largest cell (qwen3.5-122b, p=0.222) sits inside the GPT-4.1 AIME accuracy range and still saturates (phi=1.041). A cross-system contrast at comparable aggregate accuracy contrasts near-complete mechanical agreement in the open-weights models against a larger preference-unexplained residual in the frontier family. This contrast is confounded with sampling protocol by design. Agreement is graded evidence, not certification. No new voting method is proposed; code and evidence are committed.