We consider the problem of aggregating individual preferences over alternatives into a social ranking. A key feature of the problems that we consider---and the one that allows us to obtain positive results, in contrast to negative results such as Arrow's Impossibililty Theorem---is that the alternatives to be ranked are outcomes of a competitive process. Examples include rankings of colleges or academic journals. The foundation of our ranking method is that alternatives that an agent desires---those that they have been rejected by---should be ranked higher than the one they receive. We provide a mechanism to produce a social ranking given any preference profile and outcome assignment, and characterize this ranking as the unique one that satisfies certain desirable axioms.

Envy of another person's assignment is ``justified'' if you ``deserve'' the object and it is possible to assign you to the object. Currently, the literature only considers whether or not the agent deserves the object and ignores whether or not assigning her to it is possible. This paper defines a fair set of assignments in terms of what is possible. We prove that a fair set of assignments has the same properties as the set of stable matches: the Lattice Theorem, Decomposition Lemma, and Rural Hospital Theorem all hold. Moreover, there is a unique, student-optimal fair assignment: the assignment made by Kesten's Efficiency Adjusted Deferred Acceptance mechanism when all students consent.