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

Area of Science:

• Medical Education
• Algorithm Theory
• Matching Markets

Background:

• The National Resident Matching Program (NRMP) facilitates the centralized matching of medical school graduates to U.S. residency programs.
• The NRMP algorithm has evolved over 20 years to accommodate various participant requirements and match variations.
• Understanding stable matching theory is crucial for evaluating the NRMP's effectiveness.

Purpose of the Study:

• To evaluate the current NRMP matching algorithm's adequacy in fulfilling its intended purpose.
• To identify potential improvements to the NRMP matching process.
• To compare the NRMP algorithm's characteristics with theoretical findings in stable matching.

Main Methods:

• Describing the fundamental NRMP deferred-acceptance algorithm.
• Analyzing various "match variations" implemented over two decades.
• Presenting the theory of stable preference matching, including optimal matchings and preference list strategies.

Main Results:

• The NRMP algorithm produces a program-optimal stable match when no match variations are required.
• Match variations can lead to situations where no stable matching exists, potentially compromising program-optimality.
• Differences between program-optimal and applicant-optimal matchings appear small based on current evidence.

Conclusions:

• The NRMP algorithm's stability and optimality can be affected by introduced match variations.
• Further research is necessary to fully assess the impact of different stable matching algorithms on residency match outcomes.
• Ensuring the NRMP algorithm consistently achieves optimal and stable matches requires ongoing evaluation.