Lyapunov based Stochastic Stability of a Quantum Decision System for Human-Machine Interaction

TL;DR

This paper develops a stochastic Lyapunov framework to control quantum decision systems in human-machine interactions, ensuring convergence to specific decisions by dynamically adapting inputs based on quantum Lindbladian dynamics.

Contribution

It introduces a novel stochastic Lyapunov approach to control quantum decision models in human-machine systems, extending existing mathematical tools.

Findings

Quantum decision dynamics can be stabilized using Lyapunov methods.

Controller inputs can steer decisions to desired outcomes asymptotically.

The framework generalizes recent stochastic stability results.

Abstract

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.