Quickest Detection for Human-Sensor Systems Using Quantum Decision Theory

A sensor observes an underlying state of nature in noise, computes a posterior probability of this state, and provides this posterior as a recommendation to a human decision-maker. The human then makes decisions based on this recommendation. By recording these human decisions over time, how can a quickest detector detect a change in the underlying state? This paper addresses the above human-sensor interface problem. This framework generalizes classical quickest detection since the detector only has access to human decisions rather than noisy signals with known statistical properties. We utilize a Quantum Decision Theory model (widely studied in mathematical psychology) to capture peculiarities of human decision making. We provide theoretical guarantees for the quickest detector's optimal policy, such as a threshold structure, a bound on performance, robustness to variations in the decision-model parameters, and increased performance under ‘rational’ human decisions. Finally, we illustrate a numerical implementation of this quickest detector in the context of the Prisoner's Dilemma problem, in which it has been observed that Quantum Decision Theory can uniquely model empirically tested violations of the sure-thing principle.