What Does Disagreement Mean? A Semantic Identifiability Frontier for Pairwise Preference Learning

arXiv:2610.20450v1 Announce Type: cross Abstract: Pairwise comparison data are a standard supervision signal in preference learning, but disagreement in such data can reflect stable latent heterogeneity, ephemeral stochasticity, or non-binary responses hidden by a forced-choice interface. We study which of these semantic distinctions are identifiable from the feedback channel itself. We introduce a nonparametric latent semantic model with three querywise quantities: aggregate directional preference mu_q, persistent disagreement au_q, and non-binary mass alpha_q. Under the anonymous binary channel, we prove an exact semantic fiber theorem: mu_q is point-identified, whereas (au_q, alpha_q) vary over an explicit feasible region compatible with the same binary law. Same-annotator repeats identify au_q through a covariance identity, abstention-enabled feedback identifies alpha_q directly, and together they point-identify the full semantic triple. We also derive finite-sample estimators, nonasymptotic concentration bounds, and semantics-aware action-recovery guarantees, and validate the theory on theorem-matched synthetic data.

Source: arXiv cs.LG | 2026-10-15