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ARTICLE |

The Effects of the Change in the NRMP Matching Algorithm FREE

Alvin E. Roth, PhD; Elliott Peranson, MASc
[+] Author Affiliations

Corresponding author: Alvin E. Roth, PhD, Department of Economics, University of Pittsburgh, Pittsburgh, PA 15260 (e-mail: alroth+@pitt.edu).


JAMA. 1997;278(9):729-732. doi:10.1001/jama.1997.03550090053032
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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 applicantproposing 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.

REFERENCES

Peranson E, Randlett RR.  The NRMP matching algorithm revisited: theory versus practice . Acad Med . 1995;;70:477-484.
Peranson E, Randlett RR.  Comments on Williams' 'A Reexamination of the NRMP Matching Algorithm .' Acad Med . 1995;;70:490-494.
Williams KJ.  A reexamination of the NRMP matching algorithm . Acad Med . 1995;;70:470-476.
Williams, KJ.  Comments on Peranson and Randlett's 'The NRMP Matching Algorithm Revisited: Theory versus Practice .' Acad Med . 1995;;70:485-489.
American Medical Student Association and Public Citizen Health Research Group. Report on hospital bias in the NRMP [American Medical Student Association site]. September 1995. Available at: http://pubweb.acns.nwu.edu/-alan/nrmp2.html. Accessed August 1, 1997.
American Medical Association—Medical Student Section. American Medical Association—Medical Student Section resolutions for the 1995 interim meeting [Texas Medical Association Web site]. Available at: http://www.bcm.tmc.edu/ama-mss/ i95res.htm#11. Accessed August 1, 1997.
Roth AE, Sotomayor M. Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis . New York, NY: Cambridge University Press; 1990;.
Roth AE.  The evolution of the labor market for medical interns and residents: a case study in game theory . J Political Economy . 1984;;92:991-1016.
Roth AE.  New physicians: a natural experiment in market organization . Science . 1990;;250:1524-1528.
Roth AE.  The National Resident Matching Program as a labor market . JAMA . 1996;;275:1054-1056.
Gale D, Shapley L.  College admissions and the stability of marriage . Am Math Mon . 1962;;69:9-15.
Roth A.  A natural experiment in the organization of entry level labor markets: regional markets for new physicians and surgeons in the UK . Am Econ Rev . 1991;;81:415-440.
Roth A, Xing X.  Jumping the gun: imperfections and institutions related to the timing of market transactions . Am Econ Rev . 1994;;84:992-1044.
Aldershof B, Carducci OM.  Stable matchings with couples . Discrete Appl Math . 1996;;68:203-207.
Roth A. Interim report 1: evaluation of the current NRMP algorithm, and preliminary design of an applicant-processing algorithm [design review of the National Resident Matching Program home page]. March 11, 1996. Available at: http://www.pitt.edu /~alroth/interiml.html. Accessed August 1, 1997.
Roth AE, Vande Vate JH.  Random paths to stability in 2-sided matching . Econometrica . 1990;;58:1475-1480.
Roth AE. Report on the design and testing of an applicant proposing matching algorithm, and comparison with the existing NRMP algorithm [design review of the National Resident Matching Program home page]. December 6, 1996. Available at: http:/ /www.pitt.edu/~alroth/phasel.html. Accessed August 1, 1997.
Sonmez T. Manipulation via capacities in two-sided matching markets. J Econ Theory. In press.

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Peranson E, Randlett RR.  The NRMP matching algorithm revisited: theory versus practice . Acad Med . 1995;;70:477-484.
Peranson E, Randlett RR.  Comments on Williams' 'A Reexamination of the NRMP Matching Algorithm .' Acad Med . 1995;;70:490-494.
Williams KJ.  A reexamination of the NRMP matching algorithm . Acad Med . 1995;;70:470-476.
Williams, KJ.  Comments on Peranson and Randlett's 'The NRMP Matching Algorithm Revisited: Theory versus Practice .' Acad Med . 1995;;70:485-489.
American Medical Student Association and Public Citizen Health Research Group. Report on hospital bias in the NRMP [American Medical Student Association site]. September 1995. Available at: http://pubweb.acns.nwu.edu/-alan/nrmp2.html. Accessed August 1, 1997.
American Medical Association—Medical Student Section. American Medical Association—Medical Student Section resolutions for the 1995 interim meeting [Texas Medical Association Web site]. Available at: http://www.bcm.tmc.edu/ama-mss/ i95res.htm#11. Accessed August 1, 1997.
Roth AE, Sotomayor M. Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis . New York, NY: Cambridge University Press; 1990;.
Roth AE.  The evolution of the labor market for medical interns and residents: a case study in game theory . J Political Economy . 1984;;92:991-1016.
Roth AE.  New physicians: a natural experiment in market organization . Science . 1990;;250:1524-1528.
Roth AE.  The National Resident Matching Program as a labor market . JAMA . 1996;;275:1054-1056.
Gale D, Shapley L.  College admissions and the stability of marriage . Am Math Mon . 1962;;69:9-15.
Roth A.  A natural experiment in the organization of entry level labor markets: regional markets for new physicians and surgeons in the UK . Am Econ Rev . 1991;;81:415-440.
Roth A, Xing X.  Jumping the gun: imperfections and institutions related to the timing of market transactions . Am Econ Rev . 1994;;84:992-1044.
Aldershof B, Carducci OM.  Stable matchings with couples . Discrete Appl Math . 1996;;68:203-207.
Roth A. Interim report 1: evaluation of the current NRMP algorithm, and preliminary design of an applicant-processing algorithm [design review of the National Resident Matching Program home page]. March 11, 1996. Available at: http://www.pitt.edu /~alroth/interiml.html. Accessed August 1, 1997.
Roth AE, Vande Vate JH.  Random paths to stability in 2-sided matching . Econometrica . 1990;;58:1475-1480.
Roth AE. Report on the design and testing of an applicant proposing matching algorithm, and comparison with the existing NRMP algorithm [design review of the National Resident Matching Program home page]. December 6, 1996. Available at: http:/ /www.pitt.edu/~alroth/phasel.html. Accessed August 1, 1997.
Sonmez T. Manipulation via capacities in two-sided matching markets. J Econ Theory. In press.
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