An Incompatibility Between Preferential Ordering and the Decision-Theoretic Notion of Utility

A class of preferential orderings in non-monotonic logics assumes that various extensions of a model (possible worlds) can be ordered based on both their likelihood and desirability. I suggest that there is a basic incompatibility between this qualitative notion of preference and the decision-theoretic notion of utility. I demonstrate that while reasoning and decision making in the former can focus on a single state, it is meaningless in expected utility theory to say that a state or a set of states is important for a decision. This, I believe, is thought-provoking as it poses the question whether a qualitative formalism should be compatible with its quantitative counterpart or whether it can afford to be at odds with it. I discuss the difference between normative and cognitive utility and the implications of this difference for work on user interfaces to systems based on probabilistic and decision-theoretic methods. Introduction One way of looking at models of uncertain domains is th..