The Quantum Foundations of Utility

Abstract

Using the formalism of quantum theory we prove that the von Neumann entropy satisfies the conditions of the von Neumann--Morgenstern utility. We extend the entropy observable using the ensemble of statistical physics to derive a number of important functional relationships. The ensemble is then applied to an empirical study to resolve the Allais paradox and then to United States income tax data from 1996 to 2019. In both the game theoretic and econometric applications, we see that the new formalism provides significant and meaningful interpretation of real world data. What we present is a formal unification of economics from game theory, through microeconomics, and to macroeconomics.

Keywords: utility, game theory, entropy, quantum theory

JEL Classification: A12, B41, C62, C73, D58, E23