We show that an agent maximizing some utility function on a discrete (as opposed to continuous) consumption space will obey the generalized axiom of revealed preference (GARP) so long as the agent obeys cost efficiency. Cost efficiency will hold if there is some good, outside the set of goods...

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...