Estimation and Comparison Between Rank-Dependent Expected Utility, Cumulative Prospect Theory and Quantum Decision Theory

Abstract

We propose a new parametrization of Quantum Decision Theory (QDT), based on Rank Dependent Utility Theory (RDU). Using experimental data made of choices between pairs of lotteries, we compare QDT with decision theories, RDU and Cumulative Prospect Theory (CPT). At the aggregate level, calibrating together all decisions performed by all subjects (representative agent approach), we find that CPT-based QDT outperforms, with the quantum models always improving their classical counterpart. At the individual level, adopting a hierarchical maximum likelihood estimation to avoid overfitting, we classify decision makers as either RDU, RDU-based QDT, CPT or CPT-based QDT. Our major findings are the following: the quantum attraction factor plays a key role in describing subjects’ behaviors; there is a considerable heterogeneity across subjects, at odds with the representative agent approach; RDU and RDU-based QDT describe a larger fraction of subjects than CPT and CPT-based QDT, again at odds with the conclusion using the representative agent approach; a temporal stability of asset integration attitudes is found for a good fraction of the subjects; another significant fraction of subjects may be using mixtures of mental models, which are elicited selectively depending on the nature of the presented choice alternatives.