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The Benefits of Diversity: Combining Comparisons and Ratings for Efficient Scoring

Feb 08, 2026

This work addresses the challenge of effectively integrating two distinct types of preference signals—individual ratings and pairwise comparisons—to improve the accuracy of inferred entity scores. The authors propose SCoRa, a unified probabilistic graphical model that jointly learns entity scores through maximum a posteriori (MAP) estimation. They provide the first systematic theoretical demonstration that combining both signal types yields significantly better performance than methods relying on either signal alone, particularly in accurately ranking top-tier entities. Theoretical analysis establishes the model’s monotonicity and robustness, while empirical results confirm that SCoRa reliably recovers true scores even under model misspecification and consistently outperforms baseline approaches that use only ratings or only pairwise comparisons in real-world scenarios.

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Generalizing while preserving monotonicity in comparison-based preference learning models

Jun 10, 2025

Existing comparison-based preference learning models—such as those used in LLM preference modeling—often lack monotonicity guarantees: when a user explicitly prefers item *a* over *b* (*a* ≻ *b*), the model does not necessarily assign a strictly higher score to *a* and a strictly lower score to *b*. While the generalized Bradley–Terry (GBT) model is the only known monotonic formulation, it fails to generalize to unseen items. Method: We propose a linear GBT model augmented with a graph diffusion prior, enabling both strict monotonicity and cross-item generalization for the first time. By integrating embedding-space constraints and diffusion-based regularization, we derive verifiable sufficient conditions for monotonic embeddings. Contribution/Results: Experiments demonstrate that our model significantly outperforms classical GBT and non-monotonic baselines in low-data regimes, achieving superior predictive accuracy while guaranteeing controllable monotonicity—thereby resolving the long-standing trade-off between monotonicity and generalization.

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On Monotonicity in AI Alignment

Jun 10, 2025

This paper identifies a critical non-monotonicity flaw in comparative preference learning methods for AI alignment (e.g., DPO, GPO, GBT): when humans prefer outcome *y* over *z* (*y* ≻ *z*), models may paradoxically assign lower probability or reward to *y*. Method: We introduce “local pairwise monotonicity” — the first formal definition of monotonicity tailored to preference learning — and systematically formalize multiple monotonicity variants. Leveraging a generalized preference learning framework, we integrate probabilistic modeling with reward-structure analysis to derive verifiable sufficient conditions and construct a theoretical toolkit for assessing monotonic robustness. Results: Under mild assumptions, we rigorously prove that existing methods retain local monotonicity, while precisely characterizing their failure boundaries. Our analysis provides foundational theoretical guidance and practical constraints for designing more trustworthy, interpretable preference learning algorithms.

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Latest Papers

The Benefits of Diversity: Combining Comparisons and Ratings for Efficient Scoring

Feb 08, 2026

This work addresses the challenge of effectively integrating two distinct types of preference signals—individual ratings and pairwise comparisons—to improve the accuracy of inferred entity scores. The authors propose SCoRa, a unified probabilistic graphical model that jointly learns entity scores through maximum a posteriori (MAP) estimation. They provide the first systematic theoretical demonstration that combining both signal types yields significantly better performance than methods relying on either signal alone, particularly in accurately ranking top-tier entities. Theoretical analysis establishes the model’s monotonicity and robustness, while empirical results confirm that SCoRa reliably recovers true scores even under model misspecification and consistently outperforms baseline approaches that use only ratings or only pairwise comparisons in real-world scenarios.

0 citationsRead paper

Generalizing while preserving monotonicity in comparison-based preference learning models

Jun 10, 2025

Existing comparison-based preference learning models—such as those used in LLM preference modeling—often lack monotonicity guarantees: when a user explicitly prefers item *a* over *b* (*a* ≻ *b*), the model does not necessarily assign a strictly higher score to *a* and a strictly lower score to *b*. While the generalized Bradley–Terry (GBT) model is the only known monotonic formulation, it fails to generalize to unseen items. Method: We propose a linear GBT model augmented with a graph diffusion prior, enabling both strict monotonicity and cross-item generalization for the first time. By integrating embedding-space constraints and diffusion-based regularization, we derive verifiable sufficient conditions for monotonic embeddings. Contribution/Results: Experiments demonstrate that our model significantly outperforms classical GBT and non-monotonic baselines in low-data regimes, achieving superior predictive accuracy while guaranteeing controllable monotonicity—thereby resolving the long-standing trade-off between monotonicity and generalization.

0 citationsRead paper

On Monotonicity in AI Alignment

Jun 10, 2025

This paper identifies a critical non-monotonicity flaw in comparative preference learning methods for AI alignment (e.g., DPO, GPO, GBT): when humans prefer outcome *y* over *z* (*y* ≻ *z*), models may paradoxically assign lower probability or reward to *y*. Method: We introduce “local pairwise monotonicity” — the first formal definition of monotonicity tailored to preference learning — and systematically formalize multiple monotonicity variants. Leveraging a generalized preference learning framework, we integrate probabilistic modeling with reward-structure analysis to derive verifiable sufficient conditions and construct a theoretical toolkit for assessing monotonic robustness. Results: Under mild assumptions, we rigorously prove that existing methods retain local monotonicity, while precisely characterizing their failure boundaries. Our analysis provides foundational theoretical guidance and practical constraints for designing more trustworthy, interpretable preference learning algorithms.

0 citationsRead paper