Contextuality Derived from Minimal Decision Dynamics: Quantum Tug-of-War Decision Making

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Abstract
Decision making often exhibits context dependence that challenges classical probability theory. While quantum cognition has successfully modeled such phenomena, it remains unclear whether quantum probability is merely a convenient assumption or a necessary consequence of decision dynamics. Here we present a theoretical framework in which contextuality arises generatively from physically grounded constraints on decision making. By developing a quantum extension of the Tug-of-War (TOW) model, we show that conservation-based internal state updates and measurement-induced disturbance preclude any non-contextual classical description with a single, unified internal state. Contextuality therefore emerges as a structural consequence of adaptive learning dynamics. We further show that the resulting measurement structure admits Klyachko-Can-Binicioglu-Shumovsky (KCBS)-type contextuality witnesses in a minimal single-system setting. These results indicate that quantum probability is not merely a descriptive convenience, but an unavoidable effective theory for adaptive decision dynamics.
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