A complementary approach to transitive rationalizability

In this article, we study the axiomatic foundations of revealed preference\ntheory. We define two revealed relations from the weak and strong revealed\npreference. The alternative x is preferred to y with respect to U if \nx, being available in an admissible set implies, the rejecting of y; and x is preferred to y with respect to Q if the rejecting of x implies the\nrejecting of y.\nThe purpose of the paper is to show that the strong axiom of revealed\npreference and Hansson's axiom of revealed preference can be given with\nthe help of U and Q and their extension properties.