Decomposing Wrong-Consensus Agreement in LLM Self-Consistency: A GPT-4.1 Case Study

Source

• Source name: arXiv
• Source kind: paper
• Authors / organization: Lizhuo Zhang, Mengmeng Tang, Chenfeng Long, Xiaoyong Tang, Xiang Luo
• Venue: arXiv: cs.CL
• Published: 2026-08-19
• Collected: 2026-08-20
• URL: http://arxiv.org/abs/2608.18795v1
• PDF: https://arxiv.org/pdf/2608.18795v1
• DOI: UNKNOWN
• Registry group: academic_apis_and_preprints
• Evidence role: canonical_academic_index
• Language: en
• Country / region: UNKNOWN

Plain-Language Brief

The study presents an analysis of the inconsistency in the answers provided by Large Language Models (LLMs) when using majority voting to improve accuracy. The authors propose a quantitative measure called Gamma, which helps understand the failure of this method. They decompose Gamma into two components: mechanical and preference-unexplained residual. The study finds that on certain datasets like GPQA-Diamond, the per-case answer preference explains most of the held-out test-run agreement index, while on others like AIME, a significant portion remains unexplained by the mechanical preference. The authors also find evidence of self-consistency backfire on hard questions and suggest that agreement is graded evidence, not certification.

What the Document Says

• The paper discusses the variability in the gain of majority voting over multiple LLM samples, with inconsistent results.
• A quantitative account of this failure is given using a pluralistic agreement index Gamma.
• Gamma is defined as the expected fraction of wrong run samples that agree with the consensus, normalized by a reference scale d.
• The mechanical component represents what a vote delivers given only a per-case answer preference.
• A preference-unexplained residual remains after accounting for the mechanical component.
• On GPT-4.1, the decomposition shows benchmark-associated direction but does not claim significance.
• On GPQA-Diamond, the per-case answer preference explains 81-93% of the held-out test-run agreement index.
• On AIME, the mechanical preference explains only 59-78%, with a significant residual remaining.
• A self-consistency backfire on hard questions is reproduced, with a binned voting gap as low as -0.09.
• The highest-agreement bin reaches an accuracy of only 0.42-0.83, showing that agreement is graded evidence, not certification.

Key Concepts Mentioned

• Large Language Models (LLMs)
• Majority voting
• Pluralistic agreement index Gamma
• Mechanical component
• Preference-unexplained residual
• Self-consistency backfire
• Benchmark-associated direction
• Graded evidence

Claims Made by the Document

• Majority voting over multiple LLM samples can fail to improve accuracy.
• The decomposition of Gamma shows benchmark-associated direction but does not claim significance on GPT-4.1.
• On GPQA-Diamond, the per-case answer preference explains most of the held-out test-run agreement index.
• On AIME, a significant portion of the agreement index remains unexplained by the mechanical preference.
• A self-consistency backfire on hard questions is reproduced.

Evidence Used

• The provided paper discusses the findings and evidence in detail.

Methods / Approach

• The study uses a quantitative measure called Gamma to decompose the consensus agreement in LLMs.

Limitations Stated by the Authors

• The shared-bias-dominates account over-claims that the per-case answer preference explains held-out test-run agreement index on GPQA-Diamond because it captures a wrong but attractive option all cohort members latch onto.

Limitations Noted by the Agent

Agent interpretation — not from the source.

• The study does not propose a new voting method.
• The paper does not identify whether the per-case preference is induced by shared training bias.

Open Questions

• Can other voting methods be developed to improve consistency in LLMs?
• What is the source of the shared training bias that influences the per-case preferences?

Notes for Future Q&A

May include interpretation. Labeled where it does.

• The study provides insights into the inconsistencies in majority voting over multiple LLM samples, but it does not propose a solution to these issues.

Raw Abstract / Excerpt

Majority voting over multiple LLM samples is widely used to raise answer accuracy, yet its gain varies erratically: on hard questions it can even backfire. This paper gives a quantitative account of this failure. A pluralistic agreement index Gamma is defined as the expected fraction of the samples of a wrong run that agree with the consensus, normalized by a reference scale d=(1-p)/(C-1), and is decomposed into a mechanical component (what a vote delivers given only a per-case answer preference) and a preference-unexplained residual. The mechanical null is difficulty-matched and leak-free: each case is resimulated at its own accuracy and option preference, estimated from the case's other runs, so no run predicts its own agreement. On GPT-4.1 the decomposition shows benchmark-associated direction (an observational ordering over n=4 cells per benchmark, not a significance claim). On multiple-choice GPQA-Diamond, the per-case answer preference explains 81-93% of the held-out test-run agreement index: the shared-bias-dominates account over-claims here, because a wrong but attractive option the whole cohort latches onto is captured by the per-case preference channel (whether that preference is induced by shared training bias is not identified). On open-domain AIME, the mechanical preference explains only 59-78% (21-29% if shrunk to pure noise), and a preference-unexplained residual of 1.56-2.80 Gamma units survives, which a run-level preference-heterogeneity reference more than absorbs (1.4-2.1). A self-consistency backfire on hard questions is reproduced (binned voting gap down to -0.09, coupled CI [-0.12,-0.07]), and the highest-agreement bin reaches an accuracy of only 0.42-0.83, a 1.2-3.6x lift over base rate: agreement is graded evidence, not certification. No new voting method is proposed; code and evidence are committed and reproducible.