I just uploaded a revised manuscript of “Matching with Subjective and Objective Evaluations” (co-authored with Yuanju Fang) at the SSRN. This is a short paper (just 15 pages including proofs and references!) on matching theory. It would be really great if you could take a look. I put the abstract of the paper below:

Abstract
There are matching markets in which objective evaluations such as exam scores, skill qualifications, and priorities, are available in addition to subjective evaluations over agents. To examine these situations, we extend a college admission model by allowing that colleges have two different types of ordinal rankings over students, i.e., common priority order and individual preferences. A matching is called double stable if it is both priority stable and preference stable. While the existence of a double stable matching is not always guaranteed, we provide its characterization through the existing well-known mechanisms in the literature; a double stable matching exists if and only if the resulting outcome of the serial dictatorship mechanism coincides with that of the student-proposing deferred acceptance mechanism.