Calibration of Quantum Decision Theory, Aversion to Large Losses and Predictability of Probabilistic Choices

Abstract

We present the first calibration of quantum decision theory (QDT) to an empirical data set. The data comprise 91 choices between two lotteries (two prospects) presented in 91 random pairs made by 142 subjects offered at two separated times. First, we quantitatively account for the fraction of choice reversals between the two repetitions of the decisions, using a probabilistic choice formulation in the simplest possible form with no model assumption and no adjustable parameter. The prediction of choice reversal is then refined by introducing heterogeneity between decision makers through a differentiation of the population into two similar sized groups in terms of over-confident and contrarian decision makers. This supports the first fundamental tenet of QDT, which models the choice of an option as an inherent probabilistic process, such that the probability of a choice can be expressed as the sum of its utility and attraction factors. We propose to model (a) the utility factor with a stochastic version of cumulative prospect theory (logit-CPT), and (b) the attraction factor with a constant absolute risk aversion (CARA) function. This makes logit-CPT nested in our proposed parameterisation of QDT, allowing for a precise quantitative comparison between the two theories. For this data set, the QDT model is found to perform better at both the aggregate and individual levels, and for all considered fit criteria both for the first iteration of the experiment and for predictions (second iteration). The QDT effect associated with the attraction factor is mostly appreciable for prospects with big losses. Our quantitative analysis of the experiment results supports the existence of an intrinsic limit of predictability, which is associated with the inherent probabilistic nature of choice.