Robust AI Evaluation through Maximal Lotteries

The standard way to evaluate language models on subjective tasks is through pairwise comparisons: an annotator chooses the "better" of two model responses for a given prompt. These comparisons are then aggregated into a single ranking via the Bradley–Terry (BT) framework, forcing heterogeneous preferences into a total order and violating basic social-choice desiderata. In contrast, social choice theory provides an alternative approach called maximal lotteries, which aggregates pairwise preferences without imposing any assumptions on their structure. However, we show that maximal lotteries can be highly sensitive to heterogeneity among annotators and across prompts. We introduce robust lotteries, which optimize worst-case performance under plausible shifts in the preference data. On large-scale preference datasets, robust lotteries achieve more reliable win rate guarantees across the annotator distribution and recover a stable set of top performing models.

AI leaderboards often evaluate language models by asking people to compare two answers and then aggregating these judgments into a single ranking. When preferences vary across user groups or tasks, this ranking can hide substantial tradeoffs. For example, the model that looks strongest overall may be unreliable for parts of the population. We introduce robust lotteries, a framework that summarizes evaluation outcomes as a small set of complementary models. The method chooses this set to remain competitive under plausible shifts in the mix of users, prompts, or tasks being evaluated. We prove that robust lotteries satisfy key principles, including stability under redundant model copies and efficient computation, and show empirically that they improve reliability. More broadly, our work argues that AI evaluation should reward models in a way that reflects the diversity of people and tasks these systems are meant to serve.