Decision theory and the "almost implies near" phenomenon

TL;DR

This paper shows that in decision theory, behaviors that nearly satisfy axioms imply the existence of a near-ideal utility function, bridging empirical deviations and theoretical models.

Contribution

It quantifies how close actual behavior is to standard utility models when axioms are approximately satisfied, linking empirical deviations to theoretical validity.

Findings

Small deviations from axioms imply near-standard utility functions.

Quantitative bounds relate behavioral deviations to utility approximation.

Results apply across decisions under risk, uncertainty, and intertemporal choice.

Abstract

We examine behavioral axioms in decision theory that are satisfied approximately rather than exactly. We demonstrate that in key domains -- decisions under risk, uncertainty, and intertemporal choice -- behavior that \emph{almost} satisfies an axiom implies the existence of a utility function that is \emph{near} one that adheres to the standard theoretical representation (e.g., expected utility, or exponentially discounted utility). We explicitly quantify the distance between the utility that captures actual behavior and the ideal theoretical utility as a function of the measured deviation from the axiom. This result formally connects two distinct quantitative exercises: measuring empirical deviations from theory and utilizing approximate optimization. Effectively, we show that small deviations from behavioral axioms rationalize the use of standard models as valid approximations.