Dominance plausible rule and transitivity

摘要

In qualitative decision theory, a very natural way for defining preference relations over policies (acts) -functions from a set S of states to a set X of consequences- is by using the so called Dominance Plausible Rule. In this context we need a relation > over X and a relation ≥ over V(S) (the subsets of S). Then we define ≥ as follows: f ≥ g 4(＝) [f> g] > [g > f], where [f > g] denotes the set {s G S : f(s) > g{s)}. In many cases > is a modular relation and > is a total preorder. A quite rational and desirable property for the relation over policies is transitivity. In general, the relation ≥ defined by the Dominance Plausible Rule is not transitive in spite of the transitivity of ⊿. In this work we characterize the properties of the relation > forcing the relation ≥ over policies to be transitive. All this under the hypothesis of modularity of the relation >.