Editing Decision theory (section)

===Probability theory===
Advocates for the use of probability theory point to:
*   the work of [[Richard Threlkeld Cox]] for justification of the probability axioms,
*   the [[Dutch book]] paradoxes of [[Bruno de Finetti]] as illustrative of the theoretical difficulties that can arise from departures from the probability axioms, and
*   the complete class theorems, which show that all [[admissible decision rule|admissible decision rules]] are equivalent to the Bayesian decision rule for some utility function and some [[prior distribution]] (or for the limit of a sequence of prior distributions). Thus, for every decision rule, either the rule may be reformulated as a [[Bayesian probability|Bayesian]] procedure (or a limit of a sequence of such), or there is a rule that is sometimes better and never worse.