Abstention Is Not Threshold Compliance: Stated Scoring Rules in Open Language Models

Dongsun Moon

Kalai et al. propose stating the scoring rule in the prompt with an explicit threshold t, so that a model should answer only when its probability of being correct exceeds t. We probe each requirement of compliance on shared items, in 12 checkpoints from three post-training stages of four fully open 3-8B recipes, with exploratory models up to 32B. At t = 0.75, a line limiting the reply to an answer or "I abstain" (the abstention format) raised the mean abstention rate from 20% to 91%. Yet within this format, raising t from 0.5 to 0.9 changed it by only -0.8 percentage points. Without the line, the higher threshold even lowered abstention, and up to 40% of a checkpoint's items received decisions that no compliant policy with threshold-independent beliefs could make. Given the probability that their answer was correct, the checkpoints barely responded to the threshold in a forced-choice probe. Comparisons with self-assessment signals such as P(True) depended on the grader and on answer drift between prompts. An external threshold on recalibrated P(True) made coverage non-increasing in t by construction. Calibrated on the evaluation distribution (post hoc), it beat the abstention…