Sensitivity to Subjective Expected Utility Maximization: A Methodological Study, with an Illustrative Application to LLM Decision-Making

We ask whether large language models (LLMs) merely imitate rationales when choosing between two options, or whether their choices reflect a systematic underlying decision structure. Using synthetic binary decision settings in which models choose between profiles defined by graded attributes, we compare the attribute a model says mattered most with the attribute that best explains its choice under a behavioural model fit to prior decisions. The behavioural model predicts held-out choices well, showing that model behaviour is systematically related to the visible attributes rather than being random. However, direct self-reports and a separate score-based judge recover the behaviourally inferred driver only partially. The resulting picture is neither one of arbitrary behaviour nor one of fully articulated belief - outputs are structured enough to support prediction, but explicit reasons track the recovered driver only imperfectly. This qualitative pattern persists across prompt-order and sampling perturbations, alternative behavioural models, targeted occlusion analyses, and structurally varied decision settings. We interpret this as evidence for ``superficial belief'' in LLM decision-making: models behave as if guided by probabilistic local priorities over attributes, while having only limited verbal access to the attributes that drive their decisions.

Large language models are increasingly used as surrogate models for low-data optimization, but their optimizer-facing prediction and its uncertainty remain poorly understood. We study the surrogate belief elicited from an LLM under sparse observations, showing that it depends strongly on prompt text and query protocol. We introduce an uncertainty-alignment criterion that measures whether model uncertainty tracks residual ambiguity among sample-consistent functions. Across controlled inference tasks and Bayesian optimization studies, we find that structural prompts act as effective priors, POINTWISE and JOINT querying induce different beliefs, and sequential evidence leads to non-monotonic, order-sensitive confidence updates. These effects change downstream acquisition decisions and regret, showing that elicitation protocol is part of the LLM surrogate specification, not a formatting detail.

Quantitative research across the social and behavioral sciences depends on human subject experiments that are expensive, slow, and subject to sampling bias. Here we show that pretrained large language models induce risk-equivalent estimators of conditional expectations under squared loss, establishing restricted functional risk equivalence: under squared loss, the LLM induces an estimator whose risk matches the Bayes optimal risk for squared-loss prediction of conditional expectations for any inference that depends on the data only through the conditional mean. We formalize the LLM as a misspecified functional estimator $T(\hat{P}_n)$ trained on i.i.d.\ data, decompose the estimation error into representation bias $ε_{\mathrm{rep}}$ and optimization error, and prove that under mild regularity conditions the LLM's expected error converges to the irreducible population variance plus the squared representation bias, with the representation bias bounded by the Pinsker inequality. The identifiability error $δ$ propagates into the effective bias, inflating the asymptotic risk floor. We establish restricted functional risk equivalence via a bidirectional Le Cam deficiency analysis: the forward deficiency vanishes asymptotically while the reverse deficiency is exactly zero. We provide finite-sample concentration bounds and a calibration protocol with explicit decision rules. The result is a precise, provable statement: a well-calibrated LLM achieves the Bayes-optimal risk for conditional-mean-dependent inference, bounded by explicit scope conditions. In practical applications, this means that under satisfied conditions and well-calibrated models, large language models can be used in many prediction and decision-making tasks that originally relied on human experiments, approximating near-optimal statistical inference at lower cost.