Self-consistency (SC) via majority vote is a widely used way to spend inference-time compute: sample N chains of thought, return the plurality answer. On the full GPQA Diamond benchmark (198 graduate-level science questions), majority voting reduces per-problem accuracy on a majority of problems for two instruction-tuned models from different families: 56.6% of problems for Qwen2.5-7B and 65.7% for Llama-3-8B, with Qwen the primary demonstration and Llama corroborating the direction from a near-chance baseline. The effect was pre-registered on a 151-problem confirmatory split after being observed on 47 exploratory problems, and all four confirmatory hypotheses passed. A grid oracle that routes each problem to the best N across {1, 2, 4, 8, 16, 32, 64} marks a theoretical upper bound 14 accuracy points above N = 1 for Qwen and 17 for Llama, an oracle bound requiring ground truth rather than a deployable method. No verifier-free gate reaches it: neither a plurality-agreement gate nor a token-entropy gate moves accuracy more than 0.002 from fixed-budget voting at N = 64. The mechanism is direct: confidence does not track correctness on these problems. In the highest-agreement bin the plurality answer is correct about half the time for Qwen, and for Llama that bin is less accurate than its lowest-agreement bin. We pre-register and confirm these findings on small instruction-tuned models; we do not test reasoning-native models, which we flag as the central open question.

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