Why not use a centralized matching system?
In some comparable situations, candidates are assigned to institutions using a centralized matching system. The example that we know about is the National Resident Matching Program (NRMP) for medical residencies, described at http://www.nrmp.org/ In rough outline, candidates and institutions provide rank ordered lists to the service, which then makes binding assignments attempting to maximize the preferences of all involved, essentially simultaneously (over one week). Candidates and institutions are allowed to informally communicate their general preferences to each other in advance, so the system allows for some degree of human contact and maneuver at that stage. It seems likely to us that, because of the many differences between the professions and institutions in the two cases, adapting this system to our situation would require a great deal of work. And as is evident from their website, the system requires a great deal of administration to run, and to enforce the agreements on the
