Difference-in-Differences on a Censored Rating Scale Can Manufacture an Effect: Evidence from a Pre-Registered LLM-Judge Audit

Abstract

LLM-judge audits assess bias by comparing ratings across matched conditions. Difference-in-differences designs take the rating difference between two candidate responses to each item and compare it across a manipulated attribute. Building on prior work on nonlinear difference-in-differences, we show in closed form that when ratings are bounded, a severity shift common to both responses produces an observed interaction whenever the scale bounds attenuate it unequally. We then report a pre-registered audit of 990 calls to a frozen pedagogy judge. The registered primary analysis did not detect an effect of a stated novice or advanced profile on scaffolding preference. The only nominally significant secondary interaction was on the productive-struggle sub-score ($+0.378$ points; $p = 0.002$). A post-hoc construction with zero differential preference reproduced 79 to 85% of this interaction using the observed severity shift and the scale floor alone. The observed interaction therefore does not identify differential preference on the latent scale.