# Explaining versus Describing Human Decisions. Hilbert Space Structures in Decision Theory

## TL;DR

This paper develops a foundational approach to modeling human decision-making using quantum Hilbert space structures, aiming to provide explanatory power beyond phenomenological fits, exemplified through the Ellsberg paradox.

## Contribution

It introduces a realistic-operational foundation for decision processes and applies quantum correspondence rules to model the Ellsberg paradox, offering a foundational motivation for quantum cognition.

## Key findings

- Quantum models fit data but lack explanatory power.
- A new operational foundation for decision processes is proposed.
- Quantum Hilbert space structures are justified for cognitive modeling.

## Abstract

Despite the impressive success of quantum structures to model long-standing human judgement and decision puzzles, the {\it 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 {\it realistic-operational foundation of decision processes} using a known decision-making puzzle, the {\it 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.