# Beyond Binary Preferences: A Principled Framework for Reward Modeling with Ordinal Feedback

arXiv: https://arxiv.org/abs/2603.02232 · HTML: https://mlsanity.com/paper/2603.02232/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)

## Builds on (most cited first, 20 of 20)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [Contrastive Preference Optimization: Pushing the Boundaries of LLM Performance in Machine Translation](https://mlsanity.com/paper/2401.08417/) (2024)
- [HelpSteer2: Open-source dataset for training top-performing reward models](https://mlsanity.com/paper/2406.08673/) (2024)
- [RM-Bench: Benchmarking Reward Models of Language Models with Subtlety and Style](https://mlsanity.com/paper/2410.16184/) (2024)
- [Apple Intelligence Foundation Language Models: Tech Report 2025](https://mlsanity.com/paper/2507.13575/) (2025)
- [Reward Modeling with Ordinal Feedback: Wisdom of the Crowd](https://mlsanity.com/paper/2411.12843/) (2024)
- [How Well Can Preference Optimization Generalize Under Noisy Feedback?](https://mlsanity.com/paper/2510.01458/) (2025)
- [The Gray Area: Characterizing Moderator Disagreement on Reddit](https://mlsanity.com/paper/2601.01620/) (2026)
- [One Goal, Many Challenges: Robust Preference Optimization Amid Content-Aware and Multi-Source Noise](https://mlsanity.com/paper/2503.12301/) (2025)

## Built on by (most cited first, 3 of 3)

- [Discretizing Reward Models](https://mlsanity.com/paper/2606.21795/) (2026)
- [From Uncertain Judgments to Calibrated Rankings: Conformal Elo Estimation for LLM Evaluation](https://mlsanity.com/paper/2606.13221/) (2026)
- [JudgeArena: A Unified Framework for Reproducible LLM-Judge Evaluation](https://mlsanity.com/paper/2608.02620/) (2026)

## Abstract (arXiv)

Reward modeling is crucial for aligning large language models with human preferences, yet current approaches lack a principled mathematical framework for leveraging ordinal preference data. When human annotators provide graded preferences on a Likert scale (e.g., significantly better, better, slightly better, negligibly better), existing methods typically apply ad-hoc heuristics, such as margin terms or scaling factors, to loss functions derived from binary preference models like Bradley-Terry. These approaches lack an underlying mathematical model for how ordinal preference data is generated. We present a theoretically grounded framework that formulates reward modeling with Likert scale preferences as a discrete ordinal regression problem. We derive two loss functions from this formulation: a negative log-likelihood loss and an all-threshold loss, both of which learn threshold parameters that naturally capture the ordinal structure of preferences. Unlike existing heuristic methods that manually specify fixed margins or scaling weights, our approach learns these parameters directly from data within a coherent probabilistic framework. Experimental results on multiple benchmarks demonstrate that our ordinal regression approach consistently achieves competitive or superior performance compared to existing heuristic methods across diverse evaluation categories including chat, reasoning, and safety tasks. Our work provides the first principled mathematical framework for incorporating Likert scale preferences into reward model training, moving beyond ad-hoc modifications of binary preference models to enable more effective utilization of fine-grained human feedback.