Reference-Dependent Qualitative Models for Decision Making Under Uncertainty

The aim of this paper is to introduce and investigate a new family of purely qualitative models for decision making under uncertainty. Such models do not require any numerical representation and rely only on the definition of a preference relation over consequences and a relative likelihood relation on the set of events. Within this family, we focus on decision rules using reference levels in the comparison of acts. We investigate both the descriptive potential of such rules and their axiomatic foundations. We introduce in a Savage-like framework, a new axiom requiring that the Decision Maker's preference between two acts depends on the respective positions of their consequences relatively to reference levels. Under this assumption we determine the only possible form of the decision rule and characterize some particular instances of this rule under transitivity constraints.

[1]  Didier Dubois,et al.  Qualitative decision theory with preference relations and comparative uncertainty: An axiomatic approach , 2003, Artif. Intell..

[2]  Didier Dubois,et al.  Decision-Making under Ordinal Preferences and Comparative Uncertainty , 1997, UAI.

[3]  Phan Hong Giang,et al.  A Comparison of Axiomatic Approaches to Qualitative Decision Making Using Possibility Theory , 2001, UAI.

[4]  Didier Dubois,et al.  Qualitative Decision Theory with Sugeno Integrals , 1998, UAI.

[5]  Ronen I. Brafman,et al.  On the Foundations of Qualitative Decision Theory , 1996, AAAI/IAAI, Vol. 2.

[6]  Daniel Lehmann,et al.  Generalized Qualitative Probability: Savage revisited , 1996, UAI.

[7]  Lluis Godo,et al.  Lexicographic Refinements in the Context of Possibilistic Decision Theory , 2005, EUSFLAT Conf..

[8]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[9]  Hélène Fargier,et al.  Qualitative Decision under Uncertainty: Back to Expected Utility , 2003, IJCAI.

[10]  Didier Dubois,et al.  Possibility Theory as a Basis for Qualitative Decision Theory , 1995, IJCAI.

[11]  K. Arrow,et al.  Social Choice and Individual Values , 1951 .

[12]  P. Fishburn.  Axioms for Lexicographic Preferences , 1975 .

[13]  D. Schmeidler.  Integral representation without additivity , 1986 .

[14]  Craig Boutilier,et al.  Toward a Logic for Qualitative Decision Theory , 1994, KR.

[15]  Didier Dubois,et al.  Qualitative decision theory: from savage's axioms to nonmonotonic reasoning , 2002, JACM.

[16]  Paul Weng,et al.  Qualitative Decision Making Under Possibilistic Uncertainty: Toward more Discriminating Criteria , 2005, UAI.

[17]  D. Ellsberg.  Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .