Researchers say large language models can legally replace human participants in many social-science experiments — and they have the math to back it up.
A preprint posted to arXiv makes the case that a well-calibrated LLM acts as a near-optimal statistical estimator for the kind of conditional-mean data that social and behavioral scientists routinely collect from human subjects. The authors formalize the claim through what they call "restricted functional risk equivalence": under squared loss, an LLM's prediction error converges to the same floor as the theoretical Bayes-optimal estimator. They decompose the error into representation bias and optimization error, bound the bias using the Pinsker inequality, and provide finite-sample concentration bounds alongside a calibration protocol.
The practical upshot is significant. Human subject experiments are slow, expensive, and prone to sampling bias — a grad student's convenience sample is not the general population. If an LLM trained on internet-scale text can approximate the same conditional expectations, researchers could run orders-of-magnitude more inference at a fraction of the cost. The catch, buried in the paper's scope conditions, is that the equivalence holds only when those conditions are actually satisfied and the model is well-calibrated — two requirements that are much easier to assert than to verify in practice.
This joins a growing literature testing whether LLMs can serve as synthetic survey respondents, with prior work showing mixed results depending on demographic subgroup and question framing. The new contribution is a formal theoretical guarantee rather than an empirical observation — which is more rigorous, but also means the real-world test is still ahead.