Two-Round Voting: Improving Self-Consistency by Recycling Low-Vote Reasoning Evidence

Self-Consistency (SC) improves test-time reasoning by sampling multiple reasoning chains and voting on their final answers; however, it typically discards low-vote chains. On mathematical reasoning tasks, low-vote chains can still contain useful partial evidence and intermediate results while failing only near the final step, especially for uncertain problems where solution paths diverge. We propose Two-Round Voting for Self-Consistency, a training-free test-time framework that recycles low-vote chains. After a standard SC pass, we extract high-confidence prefixes from low-vote chains and use them as additional evidence to re-score candidates, followed by a second-round vote. The second-round signal is fused with first-round votes via a tunable weight, and a flip-possible gate triggers re-voting only when it can change the predicted answer to limit overhead. Across the AIME (1983-2003) and MATH-500 benchmarks, Two-Round Voting yields consistent gains over Self-Consistency for Qwen3 models at multiple scales, improving the accuracy-compute trade-off with matched FLOPs.