---
title: "Dominating decision rule"
chunk: 1/1
source: "https://en.wikipedia.org/wiki/Dominating_decision_rule"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T12:22:28.121748+00:00"
instance: "kb-cron"
---

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 
  
    
      
        
          δ
          
            1
          
        
      
    
    {\displaystyle \delta _{1}}
  
 and 
  
    
      
        
          δ
          
            2
          
        
      
    
    {\displaystyle \delta _{2}}
  
 be two decision rules, and let 
  
    
      
        R
        (
        θ
        ,
        δ
        )
      
    
    {\displaystyle R(\theta ,\delta )}
  
 be the risk of rule 
  
    
      
        δ
      
    
    {\displaystyle \delta }
  
 for parameter 
  
    
      
        θ
      
    
    {\displaystyle \theta }
  
. The decision rule 
  
    
      
        
          δ
          
            1
          
        
      
    
    {\displaystyle \delta _{1}}
  
 is said to dominate the rule 
  
    
      
        
          δ
          
            2
          
        
      
    
    {\displaystyle \delta _{2}}
  
 if 
  
    
      
        R
        (
        θ
        ,
        
          δ
          
            1
          
        
        )
        ≤
        R
        (
        θ
        ,
        
          δ
          
            2
          
        
        )
      
    
    {\displaystyle R(\theta ,\delta _{1})\leq R(\theta ,\delta _{2})}
  
 for all 
  
    
      
        θ
      
    
    {\displaystyle \theta }
  
, and the inequality is strict for some 
  
    
      
        θ
      
    
    {\displaystyle \theta }
  
.
This defines a partial order on decision rules; the maximal elements with respect to this order are called admissible decision rules.


== References ==