Generalized Expected Utility as a Universal Decision Rule – A Step Forward
Hélène Fargier, Pierre Pomeret-Coquot
Abstract
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 a XEU.
BibTeX
@InProceedings{pmlr-v244-fargier24a,
title = {Generalized Expected Utility as a Universal Decision Rule – A Step Forward},
author = {Fargier, H\'el\`ene and Pomeret-Coquot, Pierre},
booktitle = {Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence},
pages = {1323--1338},
year = {2024},
editor = {Kiyavash, Negar and Mooij, Joris M.},
volume = {244},
series = {Proceedings of Machine Learning Research},
month = {15--19 Jul},
publisher = {PMLR},
pdf = {https://raw.githubusercontent.com/mlresearch/v244/main/assets/fargier24a/fargier24a.pdf},
url = {https://proceedings.mlr.press/v244/fargier24a.html},
abstract = {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 a XEU.}
}