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

Abstract

Evaluating decisions made under uncertainty is hard when labeled outcomes are scarce, costly, or confounded with luck. We treat subjective expected utility (SEU) maximization as a stated standard and define a graded measure -- SEU sensitivity -- of an agent's conformity to it. The vehicle is a softmax choice model with a sensitivity parameter $\alpha$ on SEU-valued alternatives; the contribution is a sequence of identifiability results for $\alpha$ and for belief and utility parameters $(\beta, \delta)$, validated in Stan via prior predictive checks, parameter recovery, and simulation-based calibration (SBC), with finite-sample caveats intact. In the uncertain-choice-only model $m_0$, $\alpha$ is identifiable given the expected-utility vector $\eta$ and sharply recovered, while $(\beta, \delta)$ are only weakly informed: the posterior barely contracts and concentrates on a $\beta$-$\delta$ trade-off. In the extended model $m_1$, $\delta$ becomes identifiable in principle via a $\beta$-free risky block, but its practical recovery gain at realistic sample sizes is negligible (matched-count CI-width reduction under 1%), and that block yields no detected $\alpha$-precision gain at matched choice count. These are two distinct phenomena: for $\delta$, identifiability does not imply precise estimability at realistic $n$; for $\alpha$, identifiability is silent about what governs finite-$n$ precision. Marginal SBC passes for both models even where the joint posterior is weakly informed -- a demarcation we make precise. A two-by-two application (GPT-4o and Claude 3.5 Sonnet, each on insurance-claims triage and Ellsberg-style urns, with sampling temperature as the lever) runs end-to-end on real LLM choice data, detecting a structured comparative $\alpha$ effect in two of four cells.