More (but not much) on the paper “School Choice: A Mechanism Design Approach” (SC) and beyond…
Hey, at least the second author is Turkish…do you know him? HAHAHA!
In SC they propose mechanism 1: Use the College Admissions Problem and interpret school priorities (school district policies) as preferences. They state that in school choice generally, schools do not have preferences over students, rather they are indifferent. This they call the Gale-Shapely student optimal stable mechanism (SOSM). I followed the Wikipedia link in your posting last week. One issue that concerned me was the “hospitals/residents problem with couples” which allows a “set of residents” to include couples who must be assigned together (to the same hospital or a specified pair of hospitals). On Wikipedia it states that this problem is NP-complete. We want to be careful that we don’t formulate our problem in such as way as to be NP-complete!! However, I’m puzzled by this since in the paper we are looking at the imposition of district priorities such as neighbors going to the same school seems like a “couples” issue…perhaps it is because priorities such as this are not guaranteed in the placement, but, rather, preferred.
In “An alternative mechanism design approach to school choice in the United States” by Onur Kesten (also Turkish!), which is also quite interesting and references the first paper mentioned here, it states that the SOSM is “fair” but not Pareto efficient. In Proposition 1 the author states that there is no Pareto efficient and strategy-proof mechanism that selects the Pareto efficient and fair matching whenever it exists.
My (lame) excuse for this short posting is that I just took over as a sabbatical replacement as Director of our Office of Faculty Development and had to catch up on the real Director’s to do list!
I am determined to read both of the papers referred to here more closely before my next posting!
It would be great to see you on one of your trips up north. If you let me know soon what dates are feasible, I can submit one of them as a furlough day and then I can stay home to meet with you.
Let me know.