Hihi,
So, this is my name for our “new” approach! We can use one of the mechanisms we have been looking at and “weave in” or “interlace” an evaluatory step between each iteration of the mechanism followed by a reprioritization. This is really just like the Efficiency Adjusted Deferred Acceptance Mechanism, but our evaluatory step will be aimed at something other than efficiency. We need to decide what we want to measure, of course. If we have a rigorous definition of the quality(ies) we require, then we measure for that after each step. Depending on how the partial matching measures, we reprioritize the remaining students. This would have to mean that the desired properties are part of the schools’ priorities. That is, the overall outcome (distribution of students) is incorporated into the individual priority profiles of the schools. This is “benevolence” or “cooperation” rather than competition. It also means that, if we are using, say, SOSM that some students may change their priority status a number of times as they are tentatively assigned a school, and then unassigned based upon subsequent steps. In the top trading cycles, they priorities of a student would be fixed (and irrelevant) once they were assigned to a school since the assignments are permanent once they occur.
Here are some questions:
1) What are our desired properties and can we define them with rigor? Some possibilities are geometric (locational priorities, or with satellites as we’ve discussed in the past), social justice/demographic, “fairness”, etc.
2) If we do what is described above, will the process be finite? Since students could be reprioritized again and again…
3) Would this woven mechanism be efficient and/or stable, etc?
4) Does the imposition of our priorities make the outcome forgone…so, no “choice” is actually in play?
