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arXiv · 2610.20450

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

Manoj Saravanan·Rohit Kumar Salla·Shrikar Reddy Kota
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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 $μ_q$, persistent disagreement $τ_q$, and non-binary mass $α_q$. Under the anonymous binary channel, we prove an exact semantic fiber theorem: $μ_q$ is point-identified, whereas $(τ_q, α_q)$ vary over an explicit feasible region compatible with the same binary law. Same-annotator repeats identify $τ_q$ through a covariance identity, abstention-enabled feedback identifies $α_q$ 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.

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Manoj Saravanan, Rohit Kumar Salla, Shrikar Reddy Kota. 2026-10-14. What Does Disagreement Mean? A Semantic Identifiability Frontier for Pairwise Preference Learning. https://arxiv.org/abs/2610.20450

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