Large language models (LLMs) show considerable potential in simulating human attitudes and preferences. Prior work finds that LLM-generated responses can compress the range of attitudes found within populations and misrepresent particular subgroups in ways that vary across models and topics. We introduce Population Fidelity, an evaluation framework that distinguishes key conditions required for a set of LLM-generated responses to represent a population. It incorporates three dimensions: group-level accuracy, the amount of between-group variation, and the structure of that variation. We demonstrate the framework's utility in two ways. First, we reproduce a prior study of "machine bias" in LLM survey responses and apply the framework to its models and more recent ones, showing that poor representation reflects not only insufficient between-group variation but also variation assigned to the wrong groups. Second, we evaluate one proposed approach to improving models' population representativeness: cultural fine-tuning. We find that cultural fine-tuning can improve alignment with the survey center without improving the representation of within-population differences, a distinction that measures of aggregate agreement do not capture. We argue that representing a population requires models to reproduce several features of human attitudinal variation simultaneously. Our framework organizes these features and provides reusable code, data, and trained models for evaluating population fidelity across substantive domains and assessing proposed alignment methods.

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