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Horse-race between decision-making models: Quantum Decision Theory and "Classical" counterparts.

Giuseppe M. Ferro

Published Jul 26, 2018• 0 citations
OpenAlex

Abstract

In this work, we study different parametrizations of Quantum Decision Theory (QDT) using experimental data made of choices between pairs of lotteries. We then compare QDT with two of most famous classical decision theories, Rank-Dependent Utility(RDU) and Cumulative Prospect Theory(CPT). At the aggregate level, assuming homogeneous preferences across subjects, we find that CPT-based QDT wins by far. At the individual level, we classify decision makers as RDU, CPT or QDT. Our major findings are: quantum factor plays a key role in describing subjects’ behaviour; there is a considerable heterogeneity across subjects so that the classic representative agent approach would be completely wrong for this sample.

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In this work, we study different parametrizations of Quantum Decision Theory (QDT) using experimental data made of choices between pairs of lotteries. We then compare QDT with two of most famous classical decision theories, Rank-Dependent Utility(RDU) and Cumulative Prospect Theory(CPT). At the aggregate level, assuming homogeneous preferences across subjects, we find that CPT-based QDT wins by far. At the individual level, we classify decision makers as RDU, CPT or QDT. Our major findings are: quantum factor plays a key role in describing subjects’ behaviour; there is a considerable heterogeneity across subjects so that the classic representative agent approach would be completely wrong for this sample.
Using experimental data on choices between pairs of lotteries, we compare a new parameterized Quantum Decision Theory (QDT) with Rank Dependent Utility Theory (RDU) and Cumulative Prospect Theory (CPT). At the aggregate level, CPT-based QDT outperforms. At the individual level, the considerable heterogeneity across subjects is best described by the RDU-based QDT, at odds with the conclusion using the representative agent approach. The quantum attraction factor thus plays a key role in describing subjects’ behaviors at both levels. A large fraction of subjects exhibit temporal stability of asset integration attitudes. Another significant fraction of subjects are diagnosed to be using mixtures of mental models, which are elicited selectively depending on the nature of the presented choice alternatives.
Computer modeling of human decision making is of large importance for, e.g., sustainable transport, urban development, and online recommendation systems. In this paper we present a model for predicting the behavior of an individual during a binary game under different amounts of risk, gain, and time pressure. The model is based on Quantum Decision Theory (QDT), which has been shown to enable modeling of the irrational and subjective aspects of the decision making, not accounted for by the classical Cumulative Prospect Theory (CPT). Experiments on two different datasets show that our QDT-based approach outperforms both a CPT-based approach and data driven approaches such as feed-forward neural networks and random forests.
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.
Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest in cognitive processes, which makes it well suited for the study of decision making. QDT describes a decision maker's choice as a stochastic event occurring with a probability that is the sum of an objective utility factor and a subjective attraction factor. QDT offers a prediction for the average effect of subjectivity on decision makers, the quarter law. We examine individual and aggregated (group) data, and find that the results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. This article revisits the formalism of QDT along a concrete example and offers a practical guide to researchers who are interested in applying QDT to a dataset of binary lotteries in the domain of gains.
Abstract 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 parameterize the utility factor with a stochastic version of cumulative prospect theory (logit-CPT), and the attraction factor with a constant absolute risk aversion 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.
Quantum decision theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the theory of quantum measurements, which makes this approach relevant both for the description of decision making of humans and the creation of artificial quantum intelligence. General rules are formulated allowing for the explicit calculation of quantum probabilities representing the fraction of decision makers preferring the considered prospects. This provides a method to quantitatively predict decision-maker choices, including the cases of games with high uncertainty for which the classical expected utility theory fails. The approach is applied to experimental results obtained on a set of lottery gambles with gains and losses. Our predictions, involving no fitting parameters, are in very good agreement with experimental data. The use of quantum decision making in game theory is described. A principal scheme of creating quantum artificial intelligence is suggested.