Identifying Quantum Structures in the Ellsberg Paradox

TL;DR

This paper demonstrates that quantum mechanical models, specifically using complex Hilbert space formalism, effectively capture the ambiguity and contextuality in the Ellsberg paradox, providing a novel approach to decision theory.

Contribution

It introduces a quantum model for the Ellsberg paradox, showing the necessity of quantum interference and superposition to accurately represent ambiguity in economic decisions.

Findings

Quantum structures accurately model ambiguity in the Ellsberg paradox

Experimental data fit well within the quantum formalism in Hilbert space

Quantum effects are essential to describe the conceptual situation in decision-making

Abstract

Empirical evidence has confirmed that quantum effects occur frequently also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and social processes. In this paper, we elaborate a quantum mechanical model which faithfully describes the 'Ellsberg paradox' in economics, showing that the mathematical formalism of quantum mechanics is capable to represent the 'ambiguity' present in this kind of situations, because of the presence of 'contextuality'. Then, we analyze the data collected in a concrete experiment we performed on the Ellsberg paradox and work out a complete representation of them in complex Hilbert space. We prove that the presence of quantum structure is genuine, that is, 'interference' and 'superposition' in a complex Hilbert space are really necessary to describe the conceptual situation presented by Ellsberg. Moreover, our approach sheds light on 'ambiguity laden' decision processes in economics and decision theory, and allows to deal with different Ellsberg-type generalizations, e.g., the 'Machina paradox'.