I just found this application of this algorithms we studied at class in order to design markets very interesting. The main issue, I think, the decision that many families have to make most of the times is determined by how far or close the schools are from their homes, instead the quality of the process of education in each school. So, I believe in school choice as a market-based program in order to improve the quality giving the best students to the best schools in the city. There are many arguments against school choice programs, but many of them are related to the process of financing and ethical issues like What all the kids don’t get the same education?, egalitarian issues. Many countries such as the US and Chile have tried this programs, but the evidence on how much is the learning process improved is not concluding.
The paper you just attached to your post I founded it very interesting because it describes an improved process that we’ve talked in class. The most important thing is that unstable matches admits justified envy. So as the textbook says: Why insist on stability when schools can be simply proscribed by renegotiating a match by forming block pairs with students? It turns out that a threat to a match is not so much a school-student blocking pair as litigious parent. What stability rules out is justified envy. Related to this, the paper discusses that Deferred acceptance (DA) and TTC are strategy proof as direct mechanisms: truthful reporting is a weakly dominant strategy for the proposing side in DA and for individuals in TTC. The main different, the authors consider, is that DA produces an outcome that is not Pareto efficient but eliminates justified envy. An allocation eliminates justified envy if there is no blocking pair; that ism if no individual prefers another assignment over the assignment and has a higher priority at the preferred assignment. TTC is a Pareto efficient but does not eliminate justified envy. There is no mechanism that is both Pareto efficient and eliminates justified envy. Alvin Roth has shown that an allocation that is free of justified envy need to be Pareto efficient. It may be useful to say that a mechanism A1 has less justified envy that mechanism A2 if, for any problem the set of blocking pairs of A1 is a subset of the set of the blocking pairs of A2.
So, the design of this mechanism, one variation of TTC, is a formal justification for resolving the trade off between Pareto efficiency and the elimination of justified envy. The paper’s authors use New Orleans and Boston data to verified that all TTC variations have significantly less justified envy that serial dictatorship.
Finally, I think it’s important to design a mechanism that avoids in certain way justified envy, because it has several moral issues in the society, so in this example of the student’s allocation may generate a tension between parents and education authorities and that perjuries the learning process.
Abdulkadiroglu, Atila, et al. (2017) “Minimizing Justified Envy in School Choice: The Design of New Orleans’ OneApp”, NBER Working Paper No. 23265, http://www.nber.org/papers/w23265
Pancs, Romans. (2017). Lectures on Microeconomics: The Big Questions Approach. Mexico, ITAM. pp. 117-120, 139 -141.
Roth, Alvin. (1982) “The Economics of Matching: Stability and Incentives”, Mathemartics of Operation Research, No. 7, pp. 617-628.