The problem of assigning students to schools, as we discussed in class has proven to be a difficult challenge, so unfortunately there is no ideal solution. The following paper compares the TTC outcomes with a DA simplified version algorithm.
In the paper “School matching in Amsterdam: Top Trading Cycles reconsidered” the author explains that, in Amsterdam, after graduating from elementary school, students have to make an important decision: what high school do they want to attend? However, this choice is even more difficult, since the capacities of the popular schools are not sufficient for the number of applicants. This leads to the complicated issue of assigning students to schools, which is one of the most studied problems in market design.
In 2015, a mechanism called Deferred Acceptance (DA) was implemented. In this algorithm, which works similarly to the Boston mechanism, students are placed according to a lottery, which is different for each school. As the paper explains, “The main difference with Boston is that the actual assignment is deferred until all the students are placed. Therefore, being elected in the first round does not guarantee a place in that particular school.” (Bruggen, 2017)
Due to DA’s work, students must submit a list of preferences, while Boston only requires a single option per round. The delivery of an extensive list of preferences is more demanding for students. For example, they have to visit more information days of the schools, which is time consuming.
As the results of the DA mechanism are not optimal, the author applies a different solution to the problem of school assignment. Compensation is needed between strategy-proofness, efficiency and equity. It is known that DA is strategy-proof and fair, but efficiency is a desirable property that should not be overlooked.
We will present the Top Trading Cycles algorithm, a mechanism that has been proven to be strategy-proof and efficient.
The paper’s main conclusion would be that each of the algorithms we discussed and analyzed has its advantages and disadvantages. When comparing DAand TTC, they create a similar task, but TTC places more students in schools for each rank in the preference list and creates an efficient Pareto assignment. TTC can adapt to the admission problem in which there are specific school priorities by applying its allocation process to only a subset of the students. TTC creates instances of justified envy, but given its properties and results it seems to fit the Amsterdam school problem better than DA
School matching in Amsterdam: VAN Bruggen, Simone, Top Trading Cycles reconsidered (July 4, 2017). Utrecht University, 1-14.