Large language models (LLMs) are rapidly being integrated into computational social science research, yet their blackboxed training and designed stochastic elements in inference pose unique challenges for scientific inquiry. This article argues that applying LLMs to social scientific tasks requires explicit assessment of uncertainty -- an expectation long established in both quantitative methodology in the social sciences and machine learning. We introduce a unified framework for evaluating LLM uncertainty based on Hill numbers, a family of diversity measures. By transforming existing uncertainty quantification (UQ) metrics into Hill numbers, the framework provides a common and intuitive scale for interpreting variation in LLM outputs while accommodating different notions of semantic similarity and different sensitivities to output distributions. We show how it might help the application of LLMs in social sciences through four empirical applications.

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