Understanding what disagreement means in preference learning data

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

Computer Science and Game TheoryMachine Learning

Summary

When people or systems give pairwise preferences—choosing one option over another—sometimes they disagree. This disagreement can come from real differences in taste, random noise, or limitations of forcing a choice between just two options. The authors study how we can tell these different causes apart using only the data itself. They introduce a mathematical model that separates stable preferences from persistent disagreement and ambiguous (non-binary) responses. Their results include ways to identify and estimate these components and show how data with repeats or abstentions can clarify what kind of disagreement is present.

What this means in practice

  • For machine learning engineers: Design preference learning systems that can distinguish between true disagreement and noise for improved decision-making.
  • For user experience researchers: Analyze pairwise user feedback data to detect when ambiguous or non-binary preferences affect choices in forced comparison tasks.

Tested on simulated data.

Authors

Manoj Saravanan, Rohit Kumar Salla, Shrikar Reddy Kota

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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