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

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.

💡 Research Summary

The paper extends the classical von Neumann‑Morgenstern (VNM) expected‑utility framework to a much broader setting by replacing the probability measure with a plausibility measure that takes values in a semiring (a set equipped with two binary operations, often denoted ⊕ and ⊗, and possibly a partial order). This semiring structure is flexible enough to encompass ordinary probabilities, possibility measures, belief functions, and other non‑additive representations of uncertainty. Within this algebraic environment the authors introduce Algebraic Expected Utility (AEU), defined for a lottery (f) as

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