How the Matching Algorithm Works

ORMS

Optometric Residency Matching Service, Inc.

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How the Matching Algorithm Works

The matching process functions to simultaneously analyze every supervisor's Ranking List with respect to every applicant's Matching Form. An algorithm is employed which simulates the real life situation of a supervisor offering a position to applicants and the applicant's subsequent acceptance or rejection of those offers. The result of this match is that each candidate is placed with his/her most preferred program which does not match with an applicant placed higher on that program's ranking list. It is important to understand that ORMS does not arbitrarily or subjectively assign applicants to programs. ORMS, as an agent to both parties, simply computes "agreements to mutually commit" between the parties based upon the objective algorithm.

With the algorithm used by ORMS, applicants gain no benefit by listing programs in any order other that their true preferences. On the matching form, placing a less preferred program above a more preferred would increase the chances of matching with the less preferred program.

To reiterate, applicants should rank their preferences based upon their true preferences. Applicants who rank programs in any other order are reducing their chances of matching with their most preferred programs and increasing the chances of matching with less preferred programs. If this is a choice which they wish to make, ORMS will honor their choice.

Supervisor's Ranking List

Applicant's Matching Form

Residency North

1 - Ed

2 - Corinne (Match)

3 - Fay

Corinne

1 - Residency East

2 - Residency North (Match)

Residency South

1 - Dave (Match)

2 - Ed

3 - Faye

Dave

1 - Residency West

2 - Residency East

3 - Residency South (Match)

Residency East

1 - Faye (Match)

2 - Corinne

1 - Residency West (Match)

2 - Residency North

3 - Residency East

4 - Residency South

Residency West

1 - Faye

2 - Ed (Match)

3 - Dave

4 - Corinne

Faye

1 - Residency East (Match)

Residency North's first choice is Ed, and Ed ranked Residency North second: a potential match, i.e., pending the matching status of Ed's first choice.
Residency South's first choice is Dave, and Dave ranked Residency South third: a potential match, i.e., pending the matching status of Dave's first two choices.
Residency East's first choice is Faye, and Faye ranked Residency East first: a match.
Residency West's first choice is Faye, and Faye matched with Residency East. Residency West's next most preferred choice is Ed, and Ed ranked West first: a match.
The potential match between Residency North and Ed is cancelled because Ed matched with a more preferred choice: Residency West. The next choice for Residency North is Corinne. Her first choice has been matched. Her second choice is Residency North: a match.
The potential match between Residency South and Dave now becomes a match since Dave's first and second choices matched with other individuals.

Using our example, we can create a hypothetical situation to re-emphasis the importance of listing true preferences on the matching form. Suppose that instead of listing his true preferences as shown in the box, Ed listed Residency North first and Residency West second. He does so, as he correctly presumes that Residency North will rank him higher than Residency West will rank him. He incorrectly believes that this will enhance his chances of securing a position at one of his preferred programs. In this case, Ed would match with Residency North; however, if he had submitted his true preferences as in the box above, he would have matched with his true preferred program, Residency West. And if Residency West had actually matched with their first choice, Faye, Ed would still have matched with Residency North. This demonstrates that Ed gained nothing by listing other than his true preferences.

ORMS uses a tie-breaking system when a ranking by the candidates and residency coordinator results in the same total. For example, candidate A ranks program A as a 1st choice, and the program ranks her as a 2nd choice, a total of 3. Simultaneously, candidate B ranks program A as a 2nd choice, and program A ranks him as a 1st choice, a total of 3. Furthermore, candidate B did not match with his 1st choice. The position would be awarded to the candidate who ranked the program highest, candidate A. This is called a candidate-biased match. In this type of system, the candidate's ranking takes precedence over the coordinator's. A tie occurs in less than 5% of the matches annually.