Approximations of rational criteria under complete ignorance and the independence axiom

Abstract

Rational decision making under complete ignorance, a limit case of uncertainty, is defined. Through a concept of approximation, a meaning is given to a criterion almost possessing a property. Rational criteria depend almost on the sole bounds of the outcome range of each decision, they are almost continuous, they can almost possess a transitive indifference relation; however, under Savage's Independence Axiom, this last property restricts possible criteria to those which can be approximated, at least partly, by either the Maximin or the Maximax criterion.