# When Self-Consistency Backfires: Majority Vote Hurts the Majority of Hard Science Problems for Small LLMs

arXiv: https://arxiv.org/abs/2608.11403 · HTML: https://mlsanity.com/paper/2608.11403/

## Key facts

- Cited by 3 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 14 of its 20 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 14 of 14)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [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)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Models](https://mlsanity.com/paper/2307.01379/) (2023)
- [Correcting Length Bias in Neural Machine Translation](https://mlsanity.com/paper/1808.10006/) (2018)
- [Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs](https://mlsanity.com/paper/2305.11860/) (2023)
- [SAC3: Reliable Hallucination Detection in Black-Box Language Models via Semantic-aware Cross-check Consistency](https://mlsanity.com/paper/2311.01740/) (2023)
- [Too Consistent to Detect: A Study of Self-Consistent Errors in LLMs](https://mlsanity.com/paper/2505.17656/) (2025)
- [Reported Confidence in LLMs Tracks Commitment More Than Correctness](https://mlsanity.com/paper/2606.29490/) (2026)
- [UNCERTAINTY-LINE: Length-Invariant Estimation of Uncertainty for Large Language Models](https://mlsanity.com/paper/2505.19060/) (2025)

## Built on by (most cited first, 3 of 3)

- [Decomposing Wrong-Consensus Agreement in LLM Self-Consistency](https://mlsanity.com/paper/2608.18795/) (2026)
- [Reasoning Concentrates Errors, and Self-Consistency Never Notices](https://mlsanity.com/paper/2609.32035/) (2026)
- [From Discovery to Decision: Finite-Budget Recoverability in LLM Voting](https://mlsanity.com/paper/2610.01014/) (2026)

## Abstract (arXiv)

Self-consistency via majority vote reduces per-problem accuracy on most GPQA Diamond problems for small instruction-tuned models: 56.6% of problems for Qwen2.5-7B and 65.7% for Llama-3-8B. The obvious remedy is a verifier-free confidence gate. This version reports that the most natural repair also fails, and separates three signal failures that v1 treated as one. A token-entropy gate fails for a measurement reason: averaged over a chain of some 602 tokens, the statistic is a measurement of the prose rather than of confidence in the answer. On Qwen2.5-7B-Instruct-Turbo, 198 problems at 64 samples each, a sample whose answer contradicts its own problem's plurality still emits that answer at a median margin of 20.52 nats, with 75.7% above 10 nats. Both quantities were pre-registered and tested once on 69 problems no exploratory analysis had read; both passed. The unit is the whole result: pooled across the benchmark the margin separates correct from incorrect samples by +0.0604 on the fraction above 10 nats [+0.0183, +0.1017], excluding zero; per-problem and paired it does not, at -0.0168 [-0.0527, +0.0182], crossing zero. The claim is not that token log-probabilities carry no information, but that a signal with real across-question discrimination is close to useless for the within-question decision a router faces. The plurality-agreement gate's failure remains without a mechanism, and we report it as an open problem. These new claims rest on one model: a registered second-model replication was sampled and could not be evaluated, and we report that rejection rather than the result. We separately report that on hosted serverless inference at a small budget, three reasoning-native models could not be evaluated, for three separately measured reasons; all three are downloadable, so this bounds what a metered per-token API buys rather than what is knowable.