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 $\backslash delta\_1$ and $\backslash delta\_2$ be two decision rules, and let $R(\backslash theta,\; \backslash delta)$ be the risk of rule $\backslash delta$ for parameter $\backslash theta$. The decision rule $\backslash delta\_1$ is said to dominate the rule $\backslash delta\_2$ if $R(\backslash theta,\backslash delta\_1)\backslash le\; R(\backslash theta,\backslash delta\_2)$ for all $\backslash theta$, and the inequality is strict for some $\backslash theta$.{{citation|title=Data Fusion in Robotics & Machine Intelligence|first1=Mongi|last1=Abadi|last2=Gonzalez|first2=Rafael C.|publisher=Academic Press|year=1992|isbn=9780323138352|page=227|url=https://books.google.com/books?id=47kOwU1xvMMC&pg=PA227}}.

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