We present the first calibration of quantum decision theory (QDT) to a dataset of binary risky choice. We quantitatively account for the fraction of choice reversals between two repetitions of the experiment, using a probabilistic choice formulation in the simplest form without model assumption or adjustable parameters. The prediction of choice reversal is then refined by introducing heterogeneity between decision makers through their differentiation into two groups: ``majoritarian'' and ``contrarian'' (in proportion 3:1). This supports the first fundamental tenet of QDT, which models choice as an inherent probabilistic process, where the probability of a prospect can be expressed as the sum of its utility and attraction factors. We propose to parameterise the utility factor with a stochastic version of cumulative prospect theory (logit-CPT), and the attraction factor with a constant absolute risk aversion (CARA) function. For this dataset, and penalising the larger number of QDT parameters via the Wilks test of nested hypotheses, the QDT model is found to perform significantly better than logit-CPT at both the aggregate and individual levels, and for all considered fit criteria for the first experiment iteration and for predictions (second ``out-of-sample'' iteration). The distinctive QDT effect captured by the attraction factor is mostly appreciable (i.e., most relevant and strongest in amplitude) for prospects with big losses. Our quantitative analysis of the experimental results supports the existence of an intrinsic limit of predictability, which is associated with the inherent probabilistic nature of choice. The results of the paper can find applications both in the prediction of choice of human decision makers as well as for organizing the operation of artificial intelligence.

翻译：我们首次对量子决策理论（QDT）进行了校准，应用于一个二元风险选择数据集。我们利用最简单的概率选择公式（无模型假设或可调参数），定量解释了实验两次重复之间选择反转的比例。随后，通过将决策者区分为“多数派”和“逆势派”（比例为3:1），引入异质性，进一步优化了选择反转的预测。这支持了QDT的第一个基本原则，即选择本质上是一个概率过程，其中前景的概率可以表示为效用因子与吸引因子之和。我们建议采用随机化累积前景理论（logit-CPT）参数化效用因子，并使用常数绝对风险厌恶（CARA）函数参数化吸引因子。针对该数据集，并通过Wilks嵌套假设检验惩罚QDT中较多的参数数量，发现QDT模型在聚合层面和个体层面均显著优于logit-CPT，且在第一次实验迭代及预测（第二次“样本外”迭代）的所有拟合准则下均表现更优。吸引因子所捕捉到的独特QDT效应主要在大额损失的前景中体现（即，振幅最强且最相关）。我们对实验结果的定量分析支持了可预测性存在内在极限，这与选择固有的概率性质相关。本文的研究结果既可应用于人类决策者的选择预测，也可用于组织人工智能的运行。