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Optimal Top-$k$ Identification from Pairwise Comparisons
Motti Goldberger, Nils Rudi
arXiv·2026
We study the active learning problem of fixed-confidence top-$k$ identification from noisy pairwise comparisons. In this problem, an algorithm sequentially chooses pairs of items to compare, observes the outcomes, and stops when it can return the set of top-$k$ items with error probability at most $δ$. The objective is to design such a $δ$-correct procedure that minimizes the expected number of comparisons (the sample complexity). This problem falls within the broader literature on fixed-confidence pure exploration in bandit models, where a common target is asymptotic optimality: the algorithm's expected sample complexity matches the information theoretic lower bound as $δ\to 0$. Asymptotically optimal procedures have been developed for a range of fixed-confidence pure-exploration problems, however to the best of our knowledge, for top-$1$, or more generally top-$k$ identification from pairwise comparisons under latent utility models an asymptotically optimal algorithm has not been established. In this setting, we develop such an algorithm. We characterize the structure of the lower bound and formulate it as a saddle-point problem. This structure enables a computationally efficient primal-dual procedure that learns the asymptotically optimal comparison allocation online. We then construct an adaptive comparison-allocation algorithm that tracks the allocation learned by the primal-dual procedure and prove it is asymptotically optimal.
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View paper →Validating LLMs in social science: Epistemic threats and emerging norms
Meera Desai, Dallas Card, Abigail Z. Jacobs
arXiv·2026
Large language models (LLMs) are reshaping social science methodology. Researchers increasingly prompt language models to generate quantitative measurements of social concepts, for example labeling data or simulating survey responses. Yet LLMs pose methodological challenges including bias, hallucination, and brittleness across contexts, with unclear threats to validity. Standard practices and norms for addressing these challenges are still emerging. We collect and systematically analyze validation practices in a comprehensive corpus of papers from eight flagship social science journals that use LLMs as measurement instruments. We find that LLM-generated measurements frequently play a central role in empirical analyses, yet validation practices are inconsistent and limited. We outline complementary strategies for more robust validation, pointing toward better norms and standards around the use of LLMs in social science.
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