When Self-Consistency Hurts: The Hidden Cost of Majority Voting in Small Language Models

Wanrong Yang, Lingfang Li, Jun Zhang, Dominik Wojtczak

We study prompted chain-of-thought (CoT) with self-consistency (SC), i.e. sampling N traces and plurality-voting, on small language models, a regime where per-query compute budgets are tight yet SC is commonly applied with a fixed sample budget inherited from large-model practice, regardless of instance difficulty. Across two model families (Qwen-2.5-0.5B, Gemma-3-1B) at FP16 and MLX-Q4 (4-bit quantisation in Apple's MLX framework), on GSM8K and MATH-500, we run 8 per-task and 4 task-pooled experiments at n=200-400 with 1,000x paired-bootstrap confidence intervals (CIs). Our first result is an upper bound: an oracle gate deciding per prompt whether to invoke SC reaches 109-174% of always-SC's accuracy at 23-30% of its compute in all 12/12 cases, so at N=5 always-SC is dominated everywhere on our grid. That margin is exactly the rate at which SC flips correct greedy answers to wrong, here 3-10.5% of prompts, which on Qwen-Q4 x MATH-500 exceeds the wrong-to-right rate and leaves always-SC 3 pt worse than always-greedy. Our second result is a deployable approximation: a gate over greedy-pass signals skips 45-99% of SC calls, with bootstrap CI half-widths under 5 pt, removing 36-79%…