Philosophy:Dominating decision rule

Short description: Rule that is never worse and sometimes better

In decision theory, a decision rule is said to dominate another if the performance of the former is sometimes better, and never worse, than that of the latter. Formally, let [math]\displaystyle{ \delta_1 }[/math] and [math]\displaystyle{ \delta_2 }[/math] be two decision rules, and let [math]\displaystyle{ R(\theta, \delta) }[/math] be the risk of rule [math]\displaystyle{ \delta }[/math] for parameter [math]\displaystyle{ \theta }[/math]. The decision rule [math]\displaystyle{ \delta_1 }[/math] is said to dominate the rule [math]\displaystyle{ \delta_2 }[/math] if [math]\displaystyle{ R(\theta,\delta_1)\le R(\theta,\delta_2) }[/math] for all [math]\displaystyle{ \theta }[/math], and the inequality is strict for some [math]\displaystyle{ \theta }[/math].

This defines a partial order on decision rules; the maximal elements with respect to this order are called admissible decision rules.