Toward a unified theory of weakly rational choice
In weakly rational choice, the choice set need only be a subset of the optimal choices. This paper considers revealed preference based on weak rationality. Let \(\langle Q| P\rangle\) denote that \(xQy\) implies not \(yPx\), where \(Q\) and \(P\) are binary relations. This notation allows for very precise expression of axioms. Suppose that \(W\) is an indirectly revealed strict preference relation, and \(V\), a corresponding weak preference relation. Then the Generalized Weak Axiom of Revealed Preference (GWARP) is simply \(\langle V\cup W| W\rangle\). Indeed, a choice correspondence is weakly rational if and only if it satisfies GWARP. Analogous results are given for weak transitive-rationality and weak quasi-transitive-rationality.
scientific article; zbMATH DE number 554104