This paper formulates the “school choice problem” as a mechanism design (MD) problem and analyze some of the existing school choice plans in this light. They show the shortcomings of the analyzed plans and propose alternative mechanisms. They state that the problem with the existing mechanisms is “appeals by unsatisfied parents.” One of the authors has posted what appears to be lecture notes from a summer course on this subject here. They also claim that this is the first paper that addresses the problem of school choice using MD.
Two of the primary problems they state in current assignment mechanisms are a) inconsistent/inadequate/incomplete processes and b) the need for (or ability to) “play” the system in order to achieve the best outcome for their child.
They outline some other similar issues that have been analyzed using MD.
1) The allocation of dormitory rooms using “random serial dictatorship” which they say IS strategy proof but is not Pareto efficient. However, they state that this mechanism cannot be applied to school choice because of priority orderings imposed by school districts making it so that all students do not have the same access to all schools. (JSG NOTE: I wonder if, for districts that simply have a city wide “lottery” if this mechanism might work…).
2) The college admissions problem.
They define the term Stability: There should be no unmatched student-school pair (i, s) where student I prefers school s to her assignment and school s prefers student I to one or more of its admitted students. The equivalent notion for school choice is that there should be no unmatched pair where student I prefers school s to her assignment and she has a higher priority than some other student who is assigned a seat at school s.
Justified envy: Hmmm, not sure of a rigorous definition of this. It is something to be eliminated though!
They use something called the “Gale-Shapley student optimal stable mechanism” and state that it has been used in the hospital-intern market in the US.
I’m running out of time for today, but I think the paper is well worth reading. I would like to spend some time thinking about the use of some modified MD approach. Some of the problems I see right away is that the approach in this paper simply accepts the stated priorities of the districts (neighborhood, etc). They appear to assume that there will be no “justified envy” and/or parent appeals as long as the mechanism accommodates the stated priorities. They also do not sufficiently address any issues of diversity stating simply that quotas can be set and filled if desirable.
