On some ordinal models for decision making under uncertainty

In the field of Artificial Intelligence many models for decision making under uncertainty have been proposed that deviate from the traditional models used in Decision Theory, i.e. the Subjective Expected Utility (SEU) model and its many variants. These models aim at obtaining simple decision rules that can be implemented by efficient algorithms while based on inputs that are less rich than what is required in traditional models. One of these models, called the likely dominance (LD) model, consists in declaring that an act is preferred to another as soon as the set of states on which the first act gives a better outcome than the second act is judged more likely than the set of states on which the second act is preferable. The LD model is at much variance with the SEU model. Indeed, it has a definite ordinal flavor and it may lead to preference relations between acts that are not transitive. This paper proposes a general model for decision making under uncertainty tolerating intransitive and/or incomplete preferences that will contain both the SEU and the LD models as particular cases. Within the framework of this general model, we propose a characterization of the preference relations that can be obtained with the LD model. This characterization shows that the main distinctive feature of such relations lies in the very poor relation comparing preference differences that they induce on the set of outcomes.