An aggregation pass gives a language model two things: candidate solutions and another chance to answer. We ask whether the candidates improve that attempt, and whether aggregation improves on selecting an existing answer. Our candidate-free control asks the same model to solve the problem again from the problem alone, using the same decoding settings and maximum output-token allowance. On AIME-2025 and HMMT-2025, Qwen3-4B-Instruct-2507 reaches 15.5% accuracy when all four candidates are wrong, compared with 27.7% for a fresh solve. When at least two candidates are correct, the ordering reverses: 88.7% for aggregation versus 59.7% for a fresh solve. With exactly one correct candidate, the benefit remains unresolved under the specified test. Yet plurality voting reaches 96.0% in the multiple-correct regime without another model generation; its accuracy difference from aggregation is inconclusive (raw $p = 0.180$). The all-wrong accuracy loss and multiple-correct gain survive a statistical correction for adding the second benchmark, developed after data collection, and persist when fresh responses are scored by their final answers. These findings concern one 4B model, two mathematics benchmarks, and a single aggregation pass over candidates truncated at their first answer. All-wrong recovery can arise from solving the problem afresh. The fresh-solve control tests whether candidates improve accuracy. Comparing with selection asks whether the additional generation improves on an existing answer.

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