The Matching Algorithm
NRMP uses a proprietary mathematical algorithm to place applicants into their most preferred options.
The matching process begins with an attempt to match an individual to the position at an organization most preferred on that applicant’s rank list. If the individual cannot be matched to that first-choice position, an attempt is made to place the individual into the second most preferred position, and so on, until either the individual obtains a tentative match to a position or until the algorithm has considered all the individual’s choices and no match can be made.
A tentative match means an organization on the individual’s rank list also ranked that individual and either:
- the organization has an unfilled position for the individual, or
- the organization does not have an unfilled position, but the individual is more preferred by the organization than another individual who already is tentatively matched to the organization.
At first, matches are “tentative” because an individual who is matched to a position at an organization may be removed from that position later in the process to make room for an individual more preferred by the organization. When an individual is removed from a tentative match, an attempt is made by the algorithm to re-match that individual, starting from the top of the individual’s rank list. The algorithm returns to the top of the individual’s rank list to ensure that the individual is matched to the most preferred choice possible. This process is carried out for all individuals until each has either been tentatively matched to the most preferred choice possible or all choices submitted by the individual have been considered and a match could not be made.
When the process has been performed on all individual rank lists, all tentative matches become final and the matching process is complete.
The mathematical algorithm used by NRMP is recognized internationally: research on the algorithm was the basis for awarding the 2012 Nobel Prize in Economic Sciences.