Which Answers Agree? Evaluating Self-Consistency from Incomplete Logs

Majority-vote self-consistency (SC) lowers per-problem accuracy on most GPQA Diamond problems for small instruction-tuned models: on 56.6% of problems for Qwen2.5-7B and 65.7% for Llama-3-8B. An obvious fix is a verifier-free confidence gate that decides which problems to vote on. We report that the most natural version of that fix also fails, and we separate three signal failures that v1 treated as one. The token-entropy gate fails for a measurement reason: averaged over a chain of 602 tokens, entropy mostly measures fluency. The chain average sits 0.0005 nats from the non-answer average and 0.1695 nats from the answer token. So we measure confidence at the answer token itself. On Qwen2.5-7B-Instruct-Turbo (198 problems, 64 samples each), a sample that disagrees with its problem's plurality still emits its answer at a median margin of at least 20.4 nats, and at least 75.5% of such samples exceed 10 nats. Both quantities were pre-registered and tested once on 69 problems that no exploratory analysis had seen; both passed. The unit matters. Pooled across the benchmark, the margin does separate correct from incorrect samples: the fraction above 10 nats differs by +0.0586 [+0.0160, +0.0994]. Within a problem, paired, it does not: -0.0142 [-0.0501, +0.0215]. Token log-probabilities do carry information, but not for the within-question choice that self-consistency makes. The agreement gate's failure has no mechanism we can identify, and we leave it open. The new claims rest on one model: a registered replication on a second model was sampled but could not be evaluated, and we report that instead. Separately, three reasoning models could not be evaluated on hosted serverless inference at a small budget, each for a different measured reason. All three are downloadable, so this is a limit of metered APIs, not of what can be known.

Large Language Models often improve accuracy on reasoning tasks by sampling multiple Chain-of-Thought (CoT) traces and aggregating them with majority voting (MV), a test-time technique called self-consistency. When we truncate a CoT partway through and regenerate the remainder, we observe that traces with correct answers reproduce their original answer more often than traces with wrong answers. We use this difference as a reliability signal, prefix consistency, that weights each candidate answer by how often it reappears under regeneration. It requires no access to token log-probabilities or self-rating prompts. Across five reasoning models and four math and science benchmarks, prefix consistency is the best correctness predictor in most settings, and reweighting votes by it reaches Standard MV plateau accuracy at up to 21x fewer tokens (median 4.6x). Our code is available at https://github.com/naoto-iwase/prefix-consistency.

Self-consistency improves large language models by sampling multiple reasoning paths and selecting the most frequent answer, but majority voting often fails to recover correct answers that are already present among the samples. We address this limitation with Ranking-Improved Self-Consistency (RISC), which reformulates answer selection in self-consistency as a ranking problem. Instead of relying on a single uncertainty or confidence signal, RISC uses a lightweight LambdaRank model to score candidate answers with five carefully designed features that capture answer frequency, semantic centrality, and reasoning-trace consistency. We evaluate RISC on three datasets under a range of test-time budgets. Across datasets, RISC consistently achieves a better accuracy-efficiency trade-off than standard self-consistency and strong baselines, with particularly large gains on question answering benchmarks. Further analysis shows that the proposed features are individually useful and, more importantly, complementary, highlighting the value of learning to combine multiple informative signals for test-time answer selection.