Which Decisions Low-Bit Quantization Breaks, and How to Predict Them
Quantization is known to hurt below four bits, but nobody can say which of a model's decisions will change at a given bit-width. This matters most where a model acts rather than answers: a compressed agent stops calling its tools and, one bit lower, loses roughly half its safety refusals, while benchmark scores barely move. Prior work assumes the added noise has a roughly fixed size, which would make confident decisions safe. We measure the decision instead: the margin, the picked option's score minus its best alternative's, tracked before and after quantization across 16 models from 8 families under round-to-nearest, seven under AWQ, two under GPTQ and one under GGUF, at 8 down to 2 bits. The damage is proportional, not fixed in size: the margin is multiplied by a factor that collapses with bit-width (median 0.86 at 4 bits, 0.33 at 3, 0.00 at 2), which we call margin shrinkage. Contraction removes the protection a large margin affords; the model's own biases pick the direction: at 3 bits the decision to call a tool collapses toward inaction while the choice of which tool is untouched. No additive account, including one whose noise grows with the margin, wins a single damaged whether-to-call or safety cell (378 of 378). Given a condition's own constants the relation predicts held-out flip rates to a median 1.7 points, calibrated per decision (error 0.004 over 161,744 predictions), no flip used in the fit. Borrowed constants are wrong by 18-33 points at 3 bits, so the paired margin set has to be measured per model and bit-width: it locates breaking decisions without replacing measurement. At 4 bits the measurement is anchored to behaviour (the most likely token over the whole vocabulary is one of the item's two options in 85% of tool items); we treat the 2-bit floor as where the instrument stops measuring. No label-free repair we tested recovers more than one more bit does.