Dominating decision rule

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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 \delta_1 and \delta_2 be two decision rules, and let R(\theta, \delta) be the risk of rule \delta for parameter \theta. The decision rule \delta_1 is said to dominate the rule \delta_2 if R(\theta,\delta_1)\le R(\theta,\delta_2) for all \theta, and the inequality is strict for some \theta.[1]

This defines a partial order on decision rules; the maximal elements with respect to this order are called admissible decision rules.[1]


  1. ^ a b Abadi, Mongi; Gonzalez, Rafael C. (1992), Data Fusion in Robotics & Machine Intelligence, Academic Press, p. 227, ISBN 9780323138352 .