对主观预期效用最大化的敏感性：一项方法学研究，并应用于大语言模型决策
Sensitivity to Subjective Expected Utility Maximization: A Methodological Study, with an Illustrative Application to LLM Decision-Making
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中文总结 AI 辅助
研究在标记结果稀缺等情况下评估不确定性决策的难题，通过含敏感性参数α的softmax选择模型得出相关可识别性结果，应用于大语言模型决策，检测到结构化比较α效应。
中文摘要 AI 辅助
在标记结果稀缺、成本高昂或与运气混淆的情况下，评估不确定性下的决策很困难。我们将主观预期效用（SEU）最大化视为既定标准，并定义了一种分级度量——SEU敏感性，用于衡量主体对其的符合程度。通过对基于SEU值的备选方案具有敏感性参数α的softmax选择模型进行研究，得出了α以及信念和效用参数（β，δ）的一系列可识别性结果，并通过先验预测检查、参数恢复和基于模拟的校准（SBC）在Stan中进行了验证，同时保留了有限样本的注意事项。在仅包含不确定选择的模型m0中，给定预期效用向量η时α是可识别的且能快速恢复，而（β，δ）的信息则很弱；在扩展模型m1中，原则上δ可通过无β的风险块识别，但在实际样本量下其实际恢复增益可忽略不计，且该块在匹配选择计数时未检测到α精度增益。通过对GPT-4o和Claude 3.5 Sonnet在保险理赔分类和埃尔斯伯格风格瓮问题上的应用，在四个单元格中的两个中检测到了结构化的比较α效应。
英文摘要
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 $α$ on SEU-valued alternatives; the contribution is a sequence of identifiability results for $α$ and for belief and utility parameters $(β, δ)$, 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 $m_0$, $α$ is identifiable given the expected-utility vector $η$ and sharply recovered, while $(β, δ)$ are only weakly informed: the posterior barely contracts and concentrates on a $β$-$δ$ trade-off. In the extended model $m_1$, $δ$ becomes identifiable in principle via a $β$-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 $α$-precision gain at matched choice count. These are two distinct phenomena: for $δ$, identifiability does not imply precise estimability at realistic $n$; for $α$, 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 $α$ effect in two of four cells.
