An interview in (not on) Clinical Orthopaedics and Related Research, largely about resident matching

 For those  readers of this blog who may have missed the May issue of Clinical Orthopaedics and Related Research, here's an interview by the editor

A Conversation with ... Alvin E. Roth PhD, Economist, Game Theorist, and Nobel Laureate Who Improved the Modern Residency Match  by Leopold, Seth S. MD, Clinical Orthopaedics and Related Research, Volume 479(5), May 2021, p 863-866   doi: 10.1097/CORR.0000000000001758

The interview includes this long answer to a short question about the resident Match:

Seth S. Leopold MD: Many readers will dispute the idea that the Match is resistant to strategic manipulation (“gaming the system”); why do you believe it is, and why do you think this perception persists?

Alvin E. Roth PhD: That question requires a somewhat complicated answer. The Match is built around an idea of how to organize a simple labor market, and that idea had to be adapted to the complex structure of the modern medical labor force. A simple labor market would be one in which graduating medical students each seek a single position, positions are well described in advance, and applicants and residency programs can each rank-order all of their possible matches; that is, applicants can rank programs and programs can rank applicants. That simple market can be modeled mathematically, and it can be shown that a deferred acceptance algorithm with applicants proposing makes it a dominant strategy for all applicants to submit rank-order lists corresponding to their true preferences. (A dominant strategy is one in which regardless of what rank-order lists others submit, no applicant can do better than to rank residency programs in order of his or her true preferences. For instance, your chance of getting your second-choice program if your first choice rejects you is exactly the same as if you had listed your second choice first.)

"That’s a theoretical answer about a market that is quite a bit simpler than the modern market for residencies. The deferred acceptance algorithm for that simple market was studied by Gale and Shapley [8], for which Shapley shared the 2012 Nobel Prize in Economics. (I had earlier shown that in a simple market, applicants can’t profitably manipulate their rank-order lists [16].)

"The actual modern market for residencies differs from that simple market in several ways. For one thing, not all applicants are seeking a single position. This can happen for several reasons, the most important of which is that couples can enter the Match looking for pairs of jobs; in 2020, for example, more than one thousand couples submitted rank-order lists consisting of pairs of jobs. There are also many more residency programs than an applicant can submit on a rank-order list, and many more applicants than programs can interview, so decisions have to be made beforehand that are more complicated than how to order the rank-order list. These complications may also add to confusion about the Match and about how the Match algorithm works.

"Computational studies of the Match nevertheless confirm that once interviews are over and an applicant has decided what programs to apply to, it is perfectly safe to submit a rank-order list that corresponds to the applicant’s true preferences [18]. To put it another way, there is no advantage to submitting a rank-order list that differs from an applicant’s preferences (and there is a danger in submitting a different rank-order list, because the Match will use the submitted list to make matches, in order).

"This fact doesn’t seem to have yet penetrated to everyone who participates in the Match [13]. For this reason, all those who advise medical students entering the Match should increase their advising efforts around this point.

"Note that the Match is only the final part of the transition to residency (or to fellowships). That transition starts with applications and interviews and includes various kinds of signals, like exam scores and transcripts and letters of reference. While the dominant-strategy property of the Match makes that part of the process strategically simple (that is, we can confidently advise students to submit rank-order lists in order of their true preferences), the other parts of the process (what rotations to take before applying, where to apply, how to conduct yourself at interviews) are not simple at all."