(1) Much of revealed preference theory has been concerned with choices restricted to certain distinguished subsets of alternatives, in particular to a class of convex polyhedra (e.g., " budget triangles " in the two commodity case). This restriction may have some rationale for analyzing the preferences of competitive consumers, but it makes the results unusable for other types of choices, e.g., of government bureaucracies, of voters, of consumers in an imperfect market. If the restriction is removed, the axiomatic structure of revealed preference theory changes radically. This axiomatic structure is studied in Sections 2-5. In Section 6 the rationale of restricting the domain of choice functions and that of rationality conditions is critically examined.