Last year, Daniela Loustalot Knapp and Nicolien worked on a project to study matching algorithms for the school choice problem. Matching is the abstraction of a problem that arises in many real-world situations and consists of making pairs of individuals from two groups that have preferences over the other group. Examples include organ donation programs, house allocations and the school choice problem. In the school choice problem, the question is how to fairly assign kids to schools. Every year, kids going to secondary school have to submit a ranking of their preferred schools. As it happens, some schools turn out to be more popular than others. Consequently, not all kids can go to their favorite schools. To decide who gets their first choice and who doesn’t, the school boards in Amsterdam use a matching algorithm (sometimes also called ‘matching mechanisms’). In this episode, we discuss how different algorithms have varying normative properties. This means that choosing and designing matching algorithms is not just a mathematical problem. The choice for what algorithms to choose may have far-reaching effects. On whether everyone gets equal opportunities, for example. Talking about matching means talking about how to divide limited goods or places as fairly as possible.

Finally, Daniela recently wrote a thesis on justifying matching algorithms. The idea is to provide non-experts with a step-by-step explanation of why the computed assignment is a good compromise between all the agents’ preferences, grounded in a set of principles that are appealing to them. We will touch upon this in the last part of the episode.