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

Hélène Fargier, Pierre Pomeret-Coquot
Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, PMLR 244:1323-1338, 2024.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Generalized Expected Utility as a Universal Decision Rule – A Step Forward %A Hélène Fargier %A Pierre Pomeret-Coquot %B Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2024 %E Negar Kiyavash %E Joris M. Mooij %F pmlr-v244-fargier24a %I PMLR %P 1323--1338 %U https://proceedings.mlr.press/v244/fargier24a.html %V 244 %X 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.
APA
Fargier, H. & Pomeret-Coquot, P.. (2024). Generalized Expected Utility as a Universal Decision Rule – A Step Forward. Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 244:1323-1338 Available from https://proceedings.mlr.press/v244/fargier24a.html.

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