This paper explores how linear ordering can be used to implement a selection function with a restricted set of choices (a limited set of possible choices, not a complete subset). In restricted settings, constructing a selection function through relationships between alternatives is not always feasible. However, this paper demonstrates that a linear ordering of the alternative set can always construct a selection function, where the fallback value is encoded as the minimum element in the linear ordering. We present an axiom system for this selection function for the general case and for the case of union-closed input restrictions. Restricted choice structures have applications in knowledge representation and reasoning, and this paper discusses applications to theory change and abstract argumentation.