Q-SCM: A Quantum-Sequential Choice Model for Driver Mental State Evolution

Abstract

We propose a Quantum-Sequential Choice Model (Q-SCM) for modelling driver mental state evolution in interactive traffic environments. The proposed framework retains the classical latent class choice structure, but replaces the conventional class membership formulation with a quantum cognitive state model. A unique feature of this model is that the quantum component is confined to the class membership layer, while the action choice layer remains a classical RUM. The driver's latent state is represented as a two-state quantum system on the Bloch sphere including neutral and defensive states. Perceptual cues, including separation distance, closing time-to-collision (CTTC), and lane deviation induce sequential unitary rotations governed by Pauli matrices. This formulation allows the model to capture memory, phase effects, cue order dependence, and transitions between behavioural regimes that depend on prior cue history. To ensure well-behaved state evolution, we introduce three control mechanisms: a monotonicity constraint that prevents pendulum-like overshoot, a geodesic safeguard mechanism that ensures convergence toward the defensive state under sustained threat exposure, and a relaxation step that allows recovery toward the neutral baseline when the threat weakens. The model is estimated using 85,754 observations from 9,610 drivers extracted from naturalistic trajectories. The empirical results show that defensive state formation is not governed only by the instantaneous values of traffic cues, but also by the accumulated cue history and the order in which cues are processed.