Admissible

Admissible is an adjective used across disciplines to denote something that is permissible under applicable rules, standards, or conditions. The core idea is that a thing is admissible if it meets a prescribed set of criteria and is eligible for consideration or use.

In law, admissible evidence is any material that may be legally introduced at trial. Evidence must be relevant and material, and its probative value must outweigh potential prejudice or confusion. Judges can exclude evidence that is hearsay, unlawfully obtained, or otherwise inadmissible under rules of evidence. The term contrasts with inadmissible evidence, which a court rules cannot be presented to the jury.

In statistics and decision theory, an admissible estimator or decision rule is one that cannot be uniformly improved upon by another rule. More precisely, an estimator is admissible if there is no other estimator with risk less than or equal to it for all parameter values and strictly smaller for some. This concept rules out dominated procedures, but admissible rules can still be complex or counterintuitive.

In game theory, an admissible strategy is one that is not weakly dominated by any other strategy; there is no alternative strategy that yields at least as good payoffs in all possible opponent responses and strictly better in some cases. Admissible strategies are often the starting point for equilibrium analysis and rationalizability.

In set theory and mathematical logic, an admissible set is a transitive set that models a weak form of set theory, typically Kripke–Platek set theory with foundation. An ordinal α is admissible if Lα is an admissible set. Admissible ordinals are central in recursion theory and the study of the constructible universe L.