National Matching Services


Matching Algorithm

2018 ORMatch


How It Works

The matching algorithm uses the preferences stated on the Rank Order Lists submitted by applicants and programs to place individuals into positions.

Illustrative Example - Let's Run a Match

Description of the Algorithm

The algorithm starts with an attempt to place an applicant into the program that is most preferred on the applicant's list. If the applicant cannot be matched to this first choice program, an attempt is then made to place the applicant into the second choice program, and so on, until the applicant obtains a tentative match, or all the applicant's choices have been exhausted.

  • Read more detail about how the matching algorithm works

    An applicant can be tentatively matched to a program in this algorithm if the program also ranks the applicant on its Rank Order List, and either:

    • the program has an unfilled position available for the applicant. In this case there is room in the program to make a tentative match between the applicant and program. or
    • the program does not have an unfilled position, but the applicant is more preferred by the program to another applicant who is currently tentatively matched to the program. In this case the applicant who is the least preferred current match in the program is removed from the program to make room for a tentative match with the more preferred applicant.

    Matches are referred to as tentative because an applicant who is matched to a program at one point in the process may later be removed from the program, to make room for an applicant more preferred by the program, as described in the second case above. When an applicant is removed from a previous tentative match, an attempt is then made to re-match this applicant, starting from the top of this applicant's list.

    This process is carried out for all applicants, until each applicant has either been tentatively matched to the most preferred choice possible, or all choices submitted by the applicant have been exhausted. When all applicants have been considered, the matching algorithm is complete and tentative matches become final.

    At no point will applicants and programs know of the tentative matches being processed by the algorithm. Applicants and programs will only be informed of the final match that they receive once the processing is complete.

    In summary, each applicant's Rank Order List is traversed "downwards", from most preferred program to least preferred, until the first program is reached at which the applicant can be tentatively matched, or until the applicant's list of choices is exhausted. Each program accepts applicants "upwards" on its Rank Order List, continually removing less preferred matches in favor of more preferred applicants, until the program is matched to the most preferred applicants who wish to be matched to the program.

Common Misunderstandings

The following information will help resolve some common misunderstandings associated with the matching process.

    Misunderstanding #1

    The Match is a computerized assignment of applicants to programs that will interfere with or limit the freedom of choice of applicants and programs.

  • Fact #1:
    The Match does not involve an arbitrary or subjective assignment of applicants to programs.

    A program cannot be matched with an applicant who is not listed on the program's Rank Order List; similarly, an applicant cannot be matched with a program that is not listed on the applicant's Rank Order List.

    Applicants and programs are free to evaluate each other and to rank their choices according to their preferences without pressure and undue haste. The matching algorithm simply follows the instructions embodied in the Rank Order Lists to facilitate the placement of applicants into positions. However, the Match removes the time pressures from the traditional process of making offers, and accepting or rejecting offers.

    The Match does not have to be computerized. The matching algorithm itself could be completed as effectively by hand. A computer system is used only to facilitate and ensure the accuracy of the matching algorithm.


Misunderstanding #2

To ensure a match, an applicant should rank those programs which seem to prefer the applicant higher than other programs which the applicant likes more, but which may prefer other applicants. (A analogous statement could be made for a program's ranking of applicants.)

  • Fact #2:
    The likelihood of being able to obtain a position at a program, or being able to attract an applicant, should not be considered when sequencing the choices on your Rank Order List.

    Applicants and programs should make out their Rank Order Lists based on their true preferences. The likelihood of obtaining a match should not affect the sequence in which programs and applicants are ranked.

    First consider the issue from the applicant's perspective. In the matching process, attempts are made to place an applicant into a program in sequence according to the applicant's stated preferences, as shown in the illustrative example above. When attempting to place an applicant into a particular program, the only reasons an applicant will not match to the program are either the program did not rank the applicant, or the program has filled all its positions with more desirable applicants. The fact that an applicant could not match to a preferred program does not affect the applicant's chances of matching to the next program on the applicant's list. Similarly, ranking additional less preferred choices will not jeopardize or affect the applicant's chances of matching to a more preferred program.

    For example, consider the Rank Order Lists below. Suppose Program A has one position. Both Applicants X and Y feel they have a very good chance of obtaining a position at Program A. However both in fact prefer other programs, Programs C and D, where they may be less desirable.

    Program A (1 Position) Applicant X Applicant Y
    1. Applicant Y 1. Program A 1. Program C
    2. Applicant X 2. Program C 2. Program D
      3. Program D 3. Program A

    Applicant Y has listed programs according to his true preferences. Applicant X has listed programs according to likelihood of being able to obtain a position.

    In the matching algorithm, Applicant X will first be tentatively matched with Program A. Next, attempts will be made to place Applicant Y into Program C, and if that is unsuccessful, into Program D. If Applicant Y cannot match with Programs C or D, an attempt will be made to place Applicant Y into Program A. Since Program A prefers Applicant Y to its current tentative match with Applicant X, Applicant X is removed from Program A and Applicant Y is matched with Program A.

    Thus Applicant Y has not jeopardized his chances of matching with Program A by putting that program lower on his list. Similarly, Applicant X has not increased her chances of matching to Program A by putting that program higher on her list.

    Similarly for programs, when an applicant is tentatively matched to a program, the program will retain that applicant until a more preferred applicant can be placed into the program. Only then will the program reject the less preferred applicant, and only then will that applicant attempt to match to a program lower on his or her list. A program cannot be bypassed by a less-preferred program on an applicant's Rank Order List, regardless of how the two programs ranked the applicant.


Misunderstanding #3

In the Match, it is important for applicants and programs to know how they will be ranked by each other.

  • Fact #3:
    Applicants and programs should make out their Rank Order Lists based on true preferences, regardless of how they will be ranked by other participants.

    For example, consider the following sets of rankings.

    Program A (1 Position) Applicant X Applicant Y
    1. Applicant Y 1. Program A 1. Program C
    2. Applicant X 2. Program C 2. Program D
      3. Program D 3. Program A

    Suppose Program A knows that Applicant Y is not going to rank the program first. If Program A feels Applicant Y is most preferred, it does not hurt Program A to put Applicant Y first. If Applicant Y cannot be matched with Programs C or D, Applicant Y will be placed into Program A. If Applicant Y is matched with either Program C or D, Program A's chances of matching with Applicant X have not been reduced because it ranked Applicant Y first. However, if Program A lists Applicant X first because it knows Applicant X is going to list Program A first, all that will be accomplished is that Program A will lose the opportunity of matching with Applicant Y, who it feels is in fact a more preferred applicant.

    As a further extension of this logic, applicants and programs need not submit to inappropriate pressures in making out their Rank Order Lists (e.g., "I'll rank you high only if you rank me high"). Applicants and programs will not know how they are actually ranked by other parties. If, for example, a program has made this statement to an applicant, the applicant is in fact not disadvantaged by making out her list according to her true preferences. If the applicant matches to this program, the program may continue to think the applicant ranked it first, regardless of where she actually ranked the program. However, if the applicant matches to another program, the first program may not be pleased, but the applicant will in fact have received a position with a more preferred program. Therefore, trying to pressure applicants or programs into inappropriately high rankings does not necessarily help in the Match (and is a violation of the ORMatch Protocols).


Misunderstanding #4

Applicants or programs can subvert the process or "beat the system" based on how they make out their Rank Order Lists. Conversely, some applicants or programs may be treated unfairly as a result of how other applicants or programs make out their lists.

  • Fact #4:
    The only strategy that will guarantee the best result for you is to rank according to your true preferences.

    The best strategy for applicants and programs to follow is to make out their lists based on their true preferences. Any other strategy may result in a worse result for the applicant or program that did not follow this "true preferences" strategy.

    For example, consider Applicant X in the following sets of rankings.

    Program A (1 Position) Applicant X Applicant Y
    1. Applicant Y 1. Program A 1. Program C
    2. Applicant X 2. Program C 2. Program D
      3. Program D 3. Program A

    If Program A in fact lists Applicant X first, Applicant X will match to Program A, because she has listed that program as her first choice. She will not match to Program C or D, which she in fact prefers, even if either of those programs prefers her to other applicants. Thus Applicant X will obtain a position with a program she prefers less because she has not made out her list according to her true preferences.

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