Choice functions and bounded rationality

• Satisficing and threshold maximization are equivalent.
• They do not restrict the form of the underlying preference relation.
• They are equivalent to a simple relaxation of the Weak Axiom of Revealed Preference.

Bounded rationality assumes a utility function but not maximization. Simon’s version is satisficing. Another, attributable to Luce, is maximization to within a threshold of discrimination. Framed as conditions on a choice function, each with weak and strong variants, the two versions of bounded rationality have been shown to be equivalent, weak variant to weak variant, strong to strong. A finding of this paper is that, unlike classical rationality, bounded rationality does not depend on (or vary in strength with) the ordering properties of the underlying preference relation. Weak bounded rationality has been shown to be equivalent to a simple relaxation of Chernoff’s Axiom, got by changing “every  x∈C(X)x∈C(X)” to “some  x∈C(X)x∈C(X)”. Another finding of this paper is that exactly the same change turns the Weak Axiom of Revealed Preference into an equivalent of strong bounded rationality.