Week of August 24, 2009

I have been awfully busy, participating in a week-long workshop at MSRI. I do not know if I told you already, but I am on sabbatical this year, and will be coming and going between SoCal and the Bay Area for MSRI’s Fall 2009 program on Tropical Geometry. This first trip was pretty hectic and that is why I did not think about contacting you at all, but the next two times I will be here, I hope that maybe we can actually get together. Of course this all will also depend on your schedule, we will see…

So in between trying to figure out what tropical geometry is and how I can use any of it for my own agenda, and also realizing that the nice little cottage I had rented for my family was in fact a bit too rustic for us (read creepy spiders of all kinds, sizes and colors everywhere, an unusably old stove and a beautifully wild garden which turned out to be a haven for pollen which Stephan is allergic to), and making arrangements to move in the middle of our stay here to a hotel nearby, I did not get much work done on our project. But I did do some thinking, and I will jot down some of my ideas here, at least so that I can officially say I did write to our blog this week.

We finally have decided to focus on a method (mechanism design broadly speaking, and Gale-Shapley type algorithms, more specifically) and we have some references to start us off. Wikipedia has a nice summary of the Gale-Shapley algorithm for the stable marriage problem. I think that after reading this, it is more or less clear how this may be used for medical school intern placements. There is a clear imbalance between the way the algorithm benefits the men and the women in the stable marriage problem; in particular, the men get to be paired up with their first choice more or less, but the women are paired up with the lowest ranked acceptable person. I think this kind of imbalance can be understandable for our case as well. The schools/districts and the students/parents are in different sides of the selection process.

Here is a question: The imbalance in the marriage problem occurs because the men do the proposing and the women do the accepting or rejecting. If the women did the proposing and the men did the accepting and rejecting the optimality/pessimality would be reversed. (Here I am using Wikipedia’s terms:optimal roughly means that the best choice is obtained, and pessimal means the least acceptable one is). In the case of school choice, what would be the better scenario? Should the schools propose and the students/parents decide or should the process be the other way around? If we want to empower the students/parents perhaps they should do the proposing… Then again, which system would be less corruptible? It may be interesting to investigate…

OK, I will stop here. I will also introduce a new tag (mechanism design-school choice) and attach it to your earlier post.