Matching Markets Helps to Pair Residents and Hospitals and Students With Schools
In economics, there is such a phenomenon known as the matching theory which essentially describes relationships between two types of things that when matched together are mutually beneficial. An example of this is normal person to person relationships in which one person is matched to another as a spouse, partner, etc. We face matching market problems quite often in life and two areas that this is quite prevalent in are the physician-residency matter and NYC high school enrollment.
Both of these issues are addressed in Dr. Lloyd Shapely and Dr. Alvin Roth’s Nobel Prize winning matching markets algorithm which is rumored to take approximately 17 seconds to produce ideal results. What exactly is Shapely and Roth’s algorithm? For one, it is called the deferred acceptance algorithm and it produces M-stable matchings in a market with M choice makers. Every choice maker would prefer this matching to any other matchings because it is stable. This means that no matched pair would choose to break the pairing for another pair.
In terms of the resident and program matching, the algorithm matches students not only with programs, but with program directors that best match the applicant surveys. This algorithm is verified every so often by testing previous years applicants, and returning thus far, consistent results. Of these results 39% were matched to their first choice and 66% were matched to one of their top four choices. In terms of New York City school choices, 8th graders were given a list of options to choose from and they were allowed 12 ranked choices. These results yielded 48% matched to their first choice (based on interests in program) and 86% were matched to one of their top five choices.
The reason why the NYC school results may have yielded favorable matching outcomes is that prior to the introduction of the algorithm, students were placed in schools that they had no preference for because of the amount of time it took to place 30,000+ students. Also several schools didn’t even consider students who hadn’t ranked their school as a number one choice.
Here are some matching market examples of both scenarios:
