The algorithm that ended
the race for interns
In 1952, American hospitals stopped competing for medical students and handed the assignment to a single procedure. Ten years later two mathematicians wrote its theory, though no one yet saw the connection.
Offers made two years ahead
From the 1920s, the creation of residency programs in the United States set hospitals against one another in a fierce contest to recruit interns. Offers went out up to two years before training began, long before a student could be properly judged. In 1945, medical schools agreed not to release transcripts or letters of recommendation before a set date, which brought selection back to the fourth year of study.
The race then shifted to speed: the time allowed to answer an offer fell from ten days in 1945 to under twelve hours in 1950. Students had to accept on the spot, without knowing what other hospitals would offer. In 1951, delegates from 79 medical schools formed a national committee calling for another method. In 1952 the first Match took place: students and hospitals each submitted a list of preferences, and a centralized procedure sorted them out.
The principle fits in one sentence: no one gains anything by answering first. Preferences are ranked in advance, the positions are filled all together, round by round, and no commitment is final until the end. Speed stops being an advantage, and the fear of missing the offer goes with it.
Practice came before theory
In 1962, David Gale and Lloyd Shapley published "College Admissions and the Stability of Marriage," describing a deferred-acceptance procedure and showing that it always yields stable matchings, that is, with no student and hospital who would prefer each other to their assignments. In 1984, Alvin Roth established that the algorithm of the Match, in use for more than thirty years, also produces a stable result. The hospitals had found by trial and error what mathematicians would prove afterwards.
Roth also observed that in the original version the hospitals make the proposals and so obtain the best stable outcome for themselves, at the students' expense. The NRMP adopted a version in which applicants propose in 1997, applied from 1998, and Roth and Shapley received the Sveriges Riksbank Prize in Economic Sciences in 2012. Today's debates on how pupils or students are assigned to places raise the same question: who proposes, and who gets the best result?
A market that runs away with itself does not always calm down alone: sometimes its rules have to be rewritten.