# Dominating decision rule

Formally, let ${\displaystyle \delta _{1}}$ and ${\displaystyle \delta _{2}}$ be two decision rules, and let ${\displaystyle R(\theta ,\delta )}$ be the risk of rule ${\displaystyle \delta }$ for parameter ${\displaystyle \theta }$. The decision rule ${\displaystyle \delta _{1}}$ is said to dominate the rule ${\displaystyle \delta _{2}}$ if ${\displaystyle R(\theta ,\delta _{1})\leq R(\theta ,\delta _{2})}$ for all ${\displaystyle \theta }$, and the inequality is strict for some ${\displaystyle \theta }$.[1]