Regret theory, Allais' Paradox, and Savage's omelet

TL;DR

This paper introduces a regret-based decision criterion that aligns with stochastic dominance, resolves Allais' paradox, and extends to complex decision scenarios like Savage's omelet where traditional utility fails.

Contribution

It develops a general regret criterion that is consistent with stochastic dominance, transitive, and resolves classical paradoxes in decision theory.

Findings

Resolves Allais' paradox with regret criterion

Ensures transitivity through a unique regret function

Applicable to incomplete information scenarios like Savage's omelet

Abstract

We study a sufficiently general regret criterion for choosing between two probabilistic lotteries. For independent lotteries, the criterion is consistent with stochastic dominance and can be made transitive by a unique choice of the regret function. Together with additional (and intuitively meaningful) super-additivity property, the regret criterion resolves the Allais' paradox including the cases were the paradox disappears, and the choices agree with the expected utility. This superadditivity property is also employed for establishing consistency between regret and stochastic dominance for dependent lotteries. Furthermore, we demonstrate how the regret criterion can be used in Savage's omelet, a classical decision problem in which the lottery outcomes are not fully resolved. The expected utility cannot be used in such situations, as it discards important aspects of lotteries.