  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.
