We identify necessary and sufficient conditions under which a coarse data set can be coarsely rationalized by a linear order (or weak order). The conditions are easy to check, and efficient algorithms are provided. We apply our theory to investigate the observable restrictions of several...

A preference over menus is said to be an indirect preference if it is induced by a preference over the objects that make up those menus, i.e., a menu A is ranked over B whenever A contains an object that is preferred to every object in B. The basic question we address in this paper is the...