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

TL;DR

This paper demonstrates that contextuality in decision making naturally arises from physically grounded constraints within a quantum extension of the Tug-of-War model, suggesting quantum probability is essential for modeling adaptive decisions.

Contribution

It introduces a quantum decision model showing that contextuality emerges from decision dynamics, establishing quantum probability as a necessary framework for adaptive decision processes.

Findings

Contextuality arises from conservation-based decision updates.

Measurement disturbance leads to unavoidable contextuality.

KCBS-type contextuality witnesses are present in minimal settings.

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.