Despite the impressive success of quantum structures to model long-standing human judgement and decision puzzles, the quantum cognition research programme still faces challenges about its explanatory power. Indeed, quantum models introduce new parameters, which may fit empirical data without necessarily explaining them. Also, one wonders whether more general non-classical structures are better equipped to model cognitive phenomena. In this paper, we provide a realistic–operational foundation of decision processes using a known decision-making puzzle, the Ellsberg paradox, as a case study. Then, we elaborate a novel representation of the Ellsberg decision situation applying standard quantum correspondence rules which map realistic–operational entities into quantum mathematical terms. This result opens the way towards an independent, foundational, rather than phenomenological, motivation for a general use of quantum Hilbert space structures in human cognition.