Calibrated Preference Learning: The Case of Label Ranking

Abstract

Calibration, the alignment of predicted probabilities with true outcome frequencies, is essential for reliable decision-making. While extensively studied for classification and regression, calibration has not been formally addressed for probabilistic label ranking, where the goal is to predict a distribution over orderings of a label set. Naively treating rankings as classes ignores their structure and fails to capture important modalities such as pairwise and top-k predictions. We formalize calibration for label ranking and develop a hierarchy of notions covering full rankings, sub-rankings, and top-k rankings. We prove that full-rank calibration implies the others but not conversely, and sub-ranking and top-k calibration are incomparable. Empirically, we find popular label ranking models are often poorly calibrated, with substantial differences between sub-ranking and top-k metrics. Applying our framework to RLHF reward models, we find that calibration correlates strongly but not perfectly with benchmark accuracy, suggesting it captures a meaningful quality dimension beyond top-1 accuracy. These findings motivate future work on understanding the downstream effects of miscalibration and developing methods to correct it.

Cite

@inproceedings{thies2026calibrated,
  title = {Calibrated {{Preference Learning}}: {{The Case}} of {{Label Ranking}}},
  booktitle = {Proceedings of the International Conference on Machine Learning (ICML)},
  author = {Thies, Santo M. A. R. and Bengs, Viktor and Kaufmann, Timo and Vollmer, Sebastian J. and H{\"u}llermeier, Eyke},
  year = {2026}
}