Axiomatic Foundations for a Class of Generalized Expected Utility: Algebraic Expected Utility

TL;DR

This paper introduces algebraic expected utility, a generalized framework for decision-making under uncertainty, unifying various utility models and maintaining key properties like linearity and dynamic consistency.

Contribution

It provides two axiomatizations of algebraic expected utility within a semiring-based plausibility measure, unifying multiple utility models under a common framework.

Findings

Axiomatizations establish algebraic expected utility as a natural extension of expected utility.

The framework preserves properties like linearity, dynamic consistency, and autoduality.

It generalizes models such as expected utility and binary possibilistic utility.

Abstract

Expected Utility: Algebraic Expected Utility In this paper, we provide two axiomatizations of algebraic expected utility, which is a particular generalized expected utility, in a von Neumann-Morgenstern setting, i.e. uncertainty representation is supposed to be given and here to be described by a plausibility measure valued on a semiring, which could be partially ordered. We show that axioms identical to those for expected utility entail that preferences are represented by an algebraic expected utility. This algebraic approach allows many previous propositions (expected utility, binary possibilistic utility,...) to be unified in a same general framework and proves that the obtained utility enjoys the same nice features as expected utility: linearity, dynamic consistency, autoduality of the underlying uncertainty measure, autoduality of the decision criterion and possibility of modeling decision maker's attitude toward uncertainty.