Generalised Probabilistic Modelling and Improved Uncertainty Estimation in Comparative LLM-as-a-Judge

Abstract

This paper explores generalised probabilistic modelling and uncertainty estimation in comparative LLM-as-a-judge frameworks. We show that existing Product-of-Experts methods are specific cases of a broader framework, enabling diverse modelling options. Furthermore, we propose improved uncertainty estimates for individual comparisons, enabling more efficient selection and achieving strong performance with fewer evaluations. We also introduce a method for estimating overall ranking uncertainty. Finally, we demonstrate that combining absolute and comparative scoring improves performance. Experiments show that the specific expert model has a limited impact on final rankings but our proposed uncertainty estimates, especially the probability of reordering, significantly improve the efficiency of systems reducing the number of needed comparisons by $\sim$50%. Furthermore, ranking-level uncertainty metrics can be used to identify low-performing predictions, where the nature of the probabilistic model has a notable impact on the quality of the overall uncertainty.