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Lyapunov based Stochastic Stability of Human-Machine Interaction: A Quantum Decision System Approach

In mathematical psychology, decision makers are modeled using the Lindbladian equations from quantum mechanics to capture important human-centric features such as order effects and violation of the sure thing principle. We consider human-machine interaction involving a quantum decision maker (human) and a controller (machine). Given a sequence of human decisions over time, how can the controller dynamically provide input messages to adapt these decisions so as to converge to a specific decision? We show via novel stochastic Lyapunov arguments how the Lindbladian dynamics of the quantum decision maker can be controlled to converge to a specific decision asymptotically. Our methodology yields a useful mathematical framework for human-sensor decision making. The stochastic Lyapunov results are also of independent interest as they generalize recent results in the literature.