The effects of the change in the NRMP matching algorithm. National Resident Matching Program.

CONTEXT: Following 2 years of heated controversy about the resident match, the National Resident Matching Program (NRMP) recently voted to replace the existing matching algorithm with a newly designed applicant-proposing algorithm. OBJECTIVE: To design an applicant-proposing algorithm for the match and compare it with the existing NRMP algorithm to determine how many applicants and residency programs could be expected to receive better or worse matches from the 2 algorithms, how the different algorithms influence the opportunity for strategic behavior, and what advice can be given to participants. DESIGN: Computational experiments compared the newly designed applicant-proposing algorithm with the existing NRMP algorithm on the rank order lists (ROLs) submitted by all applicants and residency programs in the 1987 and 1993 through 1996 NRMP matches. RESULTS: Differences in the matchings produced by the 2 algorithms are small: fewer than 1 in 1000 applicants would have received a different match. Most (but not all) of the few applicants who are matched to different positions by the 2 algorithms do better when the applicant-proposing algorithm is used; the opposite is true for programs. Opportunities for profitable strategic behavior are very rare for both applicants and programs under either algorithm. With either algorithm, both applicants and programs can be advised that trying to get a preferred match by behaving strategically is far more likely to harm than to help them. CONCLUSIONS: The existing NRMP algorithm and the newly designed applicant-proposing algorithm perform similarly. Both algorithms make it sensible for applicants and residency programs to arrange their ROLs based solely on their preferences for possible matches. The choice of algorithms will systematically affect the matches of only a small group of applicants (<0.1%). The NRMP's recent decision to use the applicant-proposing algorithm starting in 1998 reflects a judgment about the impact of this difference on applicants and programs.

The NRMP matching algorithm revisited: theory versus practice. National Resident Matching Program.

The authors examine the algorithm used by the National Resident Matching Program (NRMP) in its centralized matching of applicants to U.S. residency programs ("the Match"). Their goal is to evaluate the current NRMP matching algorithm to determine whether it still fulfills its intended purpose adequately and whether changes could be made that would improve the Match. They describe the basic NRMP algorithm and many of the variations of the matching process ("match variations") incorporated over the last 20 years to meet participants' requirements. An overview of the current state of the theory of preference matching is presented, including descriptions of the characteristics of stable matches in general, program-optimal and applicant-optimal matchings, and strategies for formulating preference lists. The characteristics of the current NRMP algorithm are then compared with the theoretical findings. Research conducted long after the original NRMP algorithm was devised has shown that an algorithm that produces stable matches is the best approach for matching applicants to positions. In the absence of requirements to satisfy match variations, the NRMP's deferred-acceptance algorithm produces a program-optimal stable match. When match variations, such as those handled by the NRMP, must be introduced, it is possible that no stable matching exists, and the resulting matching produced by the NRMP algorithm may not be program-optimal. The question of program-optimal versus applicant-optimal matchings is discussed. Theoretical and empirical evidence currently available suggest that differences between these two kinds of matchings are likely to be small. However, further tests and research are needed to assess the real differences in the results produced by different stable matching algorithms that produce program-optimal or applicant-optimal stable matches.(ABSTRACT TRUNCATED AT 250 WORDS)