Decision Theory with a Hilbert Space as Possibility Space

TL;DR

This paper introduces a decision theory framework using Hilbert space as the possibility space, aiming to address classical paradoxes like Ellsberg's within a quantum-inspired approach.

Contribution

It offers a novel interpretation of quantum Hilbert space in decision theory, extending Savage's SEU framework to better handle ambiguity and paradoxes.

Findings

Successfully models Ellsberg paradox using Hilbert space

Provides a quantum-inspired decision framework that addresses ambiguity

Bridges quantum theory and classical decision models

Abstract

In this paper, we propose an interpretation of the Hilbert space method used in quantum theory in the context of decision making under uncertainty. For a clear comparison we will stay as close as possible to the framework of SEU suggested by Savage. We will use the Ellsberg-paradox to illustrate the potential of our approach to deal with well-known paradoxa of decision theory.