A Quantum Model for the Ellsberg and Machina Paradoxes

TL;DR

This paper introduces a quantum model in Hilbert space to address the Ellsberg and Machina paradoxes, providing a novel approach to decision-making under uncertainty that surpasses traditional expected utility theories.

Contribution

It develops a quantum framework that models the Machina paradox, which existing generalizations of expected utility fail to capture.

Findings

Successfully models the Machina paradox using quantum theory

Provides a unified quantum approach for Ellsberg and Machina situations

Demonstrates limitations of classical expected utility models

Abstract

The Ellsberg and Machina paradoxes reveal that expected utility theory is problematical when real subjects take decisions under uncertainty. Suitable generalizations of expected utility exist which attempt to solve the Ellsberg paradox, but none of them provides a satisfactory solution of the Machina paradox. In this paper we elaborate a quantum model in Hilbert space describing the Ellsberg situation and also the Machina situation, and show that we can model the specific aspect of the Machina situation that is unable to be modeled within the existing generalizations of expected utility.