D&D Matching Algorithm for the Academy of Nutrition and Dietetics
Applicants submit rank order lists of internships (aka ADA programs).
Internships submit rank order lists of applicants with the maximum number of matched applicants (class size) they can accept.
Impossible matches are removed from initial rank order lists creating initial ‘adjusted’ rank order lists. Further references to lists should be considered to be ‘adjusted’ lists.
- Applicants are removed from internship lists if the applicant did not rank the internship.
- Internships are removed from applicant lists if the internship did not rank the applicant.
- Rank order lists become adjusted rank order lists after applicants and internships bubble up to fill holes.
An internship's match 'window' includes its highest ranked applicants, equal in number to their class size.
A match happens when an applicant’s highest ranked internship includes the applicant in the internship's window.
When a MATCH is made:
- The matched applicant is removed from other internship lists.
- The number of unmatched applicants in the internship's window decreases by one.
- The matched internship is removed from other applicant lists if the internship's window has no remaining unmatched applicants.
During Round 1, all unmatched applicants are considered for a match to their first rank order internship, cycling over and over through all unmatched applicants, until additional matches cannot be made.
During Round 2, all unmatched applicants are considered for a match to their first and second rank order internships, in that order, cycling over and over through all unmatched applicants until additional matches cannot be made.
During Round 3, all unmatched applicants are considered for a match to their first, second and third rank order internships, in that order, cycling over and over through all unmatched applicants until additional matches cannot be made.
Rounds 4, 5, etc. follow in like manner.
Applicant matches to internships are no longer possible when their internship list is empty,
Internship matches to applicants are no longer possible when their
- class is full.
- applicant list is empty.
Matching concludes when additional applicant-internship matches cannot be made.
FACT:
- Guaranteed matches only occur when an applicant’s initial adjusted highest rank order internship also has the applicant in the internship's initial adjusted match window of rank ordered applicants.
- All other matches depend on the sequence (order) in which matches occur.
- Withdraw When an applicant withdraws, their rank order list of internship is removed and they cannot re-enter the match.
- Online matches are binding.
RECOMMENDATIONS:
- Rankings should be based on true preferences.
- Do not second guess rank order lists.
- A more preferred match might be lost
- Participants should only rank internships they are willing to accept as interns.
- Internships should only rank applicants they are willing to accept as interns.
- Rankings are confidential and should not be shared before or after matching.