Generalized Expected Utility as a Universal Decision Rule -A Step Forward

Hélène Fargier (1, 2, 3) , Pierre Pomeret-Coquot (1, 2)

1 UT - Université de Toulouse
2 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
3 CNRS - Centre National de la Recherche Scientifique

In order to capture a larger range of decision rules, this paper extends the seminal work of [Friedman and Halpern, 1995, Chu and Halpern, 2003, 2004] about Generalized Expected Utility. We introduce the notion of algebraic mass function (and of algebraic Möbius transform) and provide a new algebraic expression for expected utility based on such functions. This utility, that we call “XEU”, generalizes Chu and Halpern’s GEU to non-decomposable measures and allows for the representation of several rules that could not be captured up to this point, and noticeably, of the Choquet integral. A representation theorem is provided that shows that only a very weak condition is needed for a rule in order to be representable as an XEU.

Mots clés: Decision theory; Preference Relation; Uncertain Reasoning; Decision Making under Uncertainty; Generalized Expected Utility; Non-additive capacities; Algebraic mass function; Choquet integral; Sugeno integral

Domaines: Informatique [cs]

Hélène Fargier, Pierre Pomeret-Coquot. Generalized Expected Utility as a Universal Decision Rule -A Step Forward. 40th Conference on Uncertainty in Artificial Intelligence (UAI 2024), Association for Uncertainty in Artificial Intelligence (AUAI), Jul 2024, Barcelona, Spain. ⟨hal-04647531⟩