Bits or permutations? Spending a fixed inference budget on weight precision or on option-order averaging in small local language models

Local language models can save memory by storing weights in fewer bits, and they can reduce sensitivity to the order of answer options by averaging a few reorderings. We ask whether the first makes the second worse, and which is the cheaper way to spend a fixed budget. On Qwen3-0.6B and Qwen3-1.7B with simulated round-to-nearest weight quantization (8, 6, 4 and 3 bits, fp16 reference), read from the logits of the letters A to D on ARC-Easy, ARC-Challenge, MMLU and HellaSwag (300 items each), 6 bits lose no accuracy against fp16 (they score +1.8 (+1.0 to +2.5) and +0.9 (+0.3 to +1.5) points higher, which we do not explain), and 8 bits change it by -0.7 (-1.1 to -0.3) and -0.4 (-0.7 to -0.2) points. At 4 bits the answer-slot skew rises from 0.15 to 0.53 (0.6B) and from 0.07 to 0.12 (1.7B); Gaussian noise at the same weight SNR gives 0.15 and 0.37 (two draws) and 0.19 (one draw), so the co…