# When Less Is More: Binary Feedback Can Outperform Ordinal Comparisons in Ranking Recovery

arXiv: https://arxiv.org/abs/2507.01613 · HTML: https://mlsanity.com/paper/2507.01613/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 2 of its 30 references that are in the map.
- First posted on arXiv 2 Jul 2025.

## Placed in

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

## Builds on (most cited first, 2 of 2)

- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [Personalizing Reinforcement Learning from Human Feedback with Variational Preference Learning](https://mlsanity.com/paper/2408.10075/) (2024)

## Abstract (arXiv)

Paired comparison data, where users evaluate items in pairs, play a central role in ranking and preference learning tasks. While ordinal comparison data intuitively offer richer information than binary comparisons, this paper challenges that conventional wisdom. We propose a general parametric framework for modeling ordinal paired comparisons without ties. The model adopts a generalized additive structure, featuring a link function that quantifies the preference difference between two items and a pattern function that governs the distribution over ordinal response levels. This framework encompasses classical binary comparison models as special cases, by treating binary responses as binarized versions of ordinal data. Within this framework, we show that binarizing ordinal data can significantly improve the accuracy of ranking recovery. Specifically, we prove that under the counting algorithm, the ranking error associated with binary comparisons exhibits a faster exponential convergence rate than that of ordinal data. Furthermore, we characterize a substantial performance gap between binary and ordinal data in terms of a signal-to-noise ratio (SNR) determined by the pattern function. We identify the pattern function that minimizes the SNR and maximizes the benefit of binarization. Extensive simulations and a real application on the MovieLens dataset further corroborate our theoretical findings.