Leximax Relations in Decision Making through the Dominance Plausible Rule

Abstract

In qualitative decision theory, a very natural way of defining preference relations ≽ over the policies (acts) is by using the so called Dominance Plausible Rule. To do that, we need a relation > over the consequences and a relation \(\sqsupseteq\) over the events. Very interesting axiomatic characterizations, à la Savage, have been established for these decision relations [6,7]. Namely, when the relation \(\sqsupseteq\) is a possibilistic relation. Unfortunately, this kind of decision relation is not discriminant enough. We have searched for decision rules that discriminate more than those defined through a possibilistic relation. In particular, in this work, we study decision relations defined by the Dominance Plausible Rule using a leximax relation \(\sqsupseteq\). We give an axiomatic characterization of these decision relations.KeywordsPreference RelationLinear OrderDefault RuleComplete RelationDecision RelationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.