Prospect Theory in Large Language Models: A Meta-Analysis of Loss Aversion, Diminishing Sensitivity, and Probability Weighting

Prospect theory splits risky choice into three parts: loss aversion, measured by the relative weight of losses to gains, $\lambda$ (e.g., $\lambda = 2$ implies that losses weigh twice as much as gains), diminishing sensitivity to the size of outcomes (i.e., the curvature and linearity of the value function), and the nonlinear weighting of probabilities.

前景理论将风险选择分为三个部分：损失厌恶（由损失与收益的相对权重 $\lambda$ 衡量，例如 $\lambda = 2$ 意味着损失的权重是收益的两倍）、对结果规模的敏感度递减（即价值函数的曲率和线性度），以及概率的非线性加权。

I examined whether Large Language Models (LLMs) display the same properties as people by meta-analyzing 102 fitted estimates from 11 studies covering 32 language models. The three components emerge differently.

我通过对涵盖 32 个语言模型的 11 项研究中的 102 个拟合估计值进行荟萃分析，考察了大型语言模型 (LLM) 是否表现出与人类相同的特性。这三个组成部分的表现各不相同。

Loss aversion is modest: the pooled $\lambda$ is 1.26 (95% CI 1.06 to 1.46), far below the strongest human meta-analytic estimate ($\lambda = 1.96$) and compatible with more conservative ones (1.07 and 1.31). Matched by design, LLMs are compatible with people when gains and losses are symmetric ($\lambda = 1.15$ against 1.07), but well below them when losses are smaller than gains (1.46 against 2.3), where human loss aversion is strongest.

损失厌恶程度适中：汇总后的 $\lambda$ 为 1.26（95% 置信区间为 1.06 至 1.46），远低于人类荟萃分析中最强的估计值（$\lambda = 1.96$），但与更保守的估计值（1.07 和 1.31）相符。在设计匹配的情况下，当收益和损失对称时，LLM 与人类的表现一致（$\lambda = 1.15$ 对比 1.07）；但当损失小于收益时（1.46 对比 2.3），LLM 的表现远低于人类，而这正是人类损失厌恶最强的时候。

Value functions are close to linear rather than concave under the Tversky-Kahneman method (1.01, against a human value of 0.67), but more concave than in people under the Tanaka method (0.52, against 0.67), so diminishing sensitivity depends on how it is measured.

在 Tversky-Kahneman 方法下，价值函数接近线性而非凹形（1.01，人类值为 0.67）；但在 Tanaka 方法下，价值函数比人类更具凹性（0.52，人类值为 0.67），因此敏感度递减取决于测量方法。

Probability weighting shows a human-like inverse S shape ($\gamma = 0.81$ under Tversky-Kahneman and 0.84 under the Tanaka method), though on few studies. In sum, LLMs show little loss aversion and little diminishing sensitivity, but retain human-like probability distortion, yet these generalizations shift when looking at specific model families and fitting methods.

概率加权呈现出类似人类的倒 S 型曲线（Tversky-Kahneman 方法下 $\gamma = 0.81$，Tanaka 方法下 $\gamma = 0.84$），尽管相关研究较少。总之，LLM 表现出的损失厌恶和敏感度递减较少，但保留了类似人类的概率扭曲；然而，当观察特定的模型系列和拟合方法时，这些概括性结论会发生变化。