Hello! Many people have contacted me with questions about the mechanics of the couples match, pointing out that whlie the NRMP web page shows how the match works for single matchees, it does not demonstrate how the couples match works. With the generous help and time of NRMP staff, I have created an example that will hopefully clarify things. Please feel free to contact me with any questions (contact info here) and hope this helps! -Jeff (AMA-MSS NRMP Liason, '99-01)

## The Match Algorithm --an example with a Couples Match

For this example, we return to the example given by the NRMP ( click here to see) with slight modifications. First, assume that City and General are on the East Coast, and Mercy and State are on the West Coast. With that in mind, Davis and Eastman, who desire to match as a couple, and based on the individual preferences used in the previous example set up the following rank order list jointly:

 Davis Eastman 1. Mercy Mercy 2. City City 3. General City 4. Mercy State 5. State Mercy 6. State Mercy 7. State State 8. General General 9. Unmatch City 10. Unmatch Mercy 11. Unmatch General

And assume the following other rank order lists, as per previous example:

 Anderson Brown Chen Ford Garcia Hassan Issacs 1. City 1. City 1. City 1. City 1. City 1. State 1. City 2. Mercy 2. Mercy 2. General 2. Mercy 2. City 2. Mercy 3. Mercy 3. State 3. Mercy 3. State 4. State 4. General 4. General 4. General

Again, each program has two open slots:

 Mercy City General State 0.5. Issacs 0.5. Issacs 0.5. Issacs 1. Chen 1. Garcia 1. Brown 1. Brown 2. Garcia 2. Hassan 2. Eastman 2. Eastman 3. Eastman 3. Hassan 3. Anderson 4. Anderson 4. Anderson 4. Chen 5. Brown 5. Chen 5. Hassan 6. Chen 6. Davis 6. Ford 7. Davis 7. Garcia 7. Davis 8. Ford 8. Garcia

The match algorithm now operates like this:

 APPLICANT TRY TO PLACE IN CURRENT PROGRAM STATUS ACTION / RESULT (Shaded boxes indicate the final matches when the process is completed.) ANDERSON 1. City City has 2 unfilled positions. Tentatively match Anderson with City. BROWN 1. City City has 1 unfilled position. Tentatively match Brown with City. CHEN 1. City City is filled with more preferred applicants. 2. Mercy Mercy has 2 unfilled positions. Tentatively match Chen with Mercy. DAVIS/EASTMAN 1. Mercy / Mercy Mercy did not rank Davis or Eastman. 2. City / City Eastman is more preferred than the current candidates, Anderson and Brown. However, Davis is not. Therefore, Davis cannot match into City. No match occurs. 3. General / City General has 2 unfilled positions; Eastman is more highly ranked than Anderson and Brown. Tentatively match Davis with General and Eastman with City; Brown must now be rematched. Since Brown has just been removed from a previous tentative match, an attempt must now be made to re-match Brown. BROWN 1. City City is filled with more preferred applicants. 2. Mercy Mercy did not rank Brown. Brown remains unmatched. FORD 1. City City is filled with more preferred applicants. 2. General General did not rank Ford. 3. Mercy Mercy did not rank Ford. 4. State State has 2 unfilled positions. Tentatively match Ford with State. GARCIA 1. City Although filled, City prefers Garcia to its least preferred current match (Anderson). Anderson is removed from City, to make room for Garcia. Tentatively match Garcia with City. Since Anderson has just been removed from a previous tentative match, an attempt must now be made to re-match Anderson. ANDERSON 1. City City is filled with more preferred applicants. Anderson remains unmatched. HASSAN 1. State State has 1 unfilled position. Tentatively match Hassan with State. ISSACS 1. City Issacs is more highly ranked than either of the current candidates, Garcia or Eastman. Issacs is tentatively matched to City and both Davis and Eastman are removed from their matches, Eastman to make room for Issacs, Davis because he is couples matching with Eastman. Tentatively match Issacs with City. Since Davis/Eastman have just been removed from a previous tentative match, an attempt must now be made to re-match them. DAVIS/EASTMAN 1. Mercy / Mercy Mercy did not rank Davis or Eastman. No match occurs. 2. City / City Neither candidate is ranked highly enough by City. No match occurs. 3. General / City General has 2 unfilled positions; Eastman is not ranked high enough by City. No match occurs. 4. Mercy / State Mercy did not rank Davis. No match occurs. 5. State / Mercy Mercy did not rank Eastman. No match occurs. 6. City / General. Davis is not ranked highly enough by City. No match occurs. 7. State / State There are no open slots at State. Of the four candidates (Davis, Eastman, Ford and Hassan) vying for the two slots, Eastman and Hassan are the two highest ranked candidates. Because only Eastman, and not Davis, can match here, no match occurs and neither is assigned State. 8. General / General General has 2 unfilled positions. Tentatively match Davis and Eastman with General.

Note very carefully the impact of matching as a couple: had they matched independently, Eastman could have matched at State, a choice higher on her personal list of preferences than her eventual match, General. However, this would have put her on the West Coast, whereas Davis would have matched at General on the East Coast.

Note also very carefully how far down the combined rank order lists we had to go to find a match. Davis and Eastman used the NRMP match well, as they listed a very large list of possible combinations, as well as several where Davis (matching in a less competitive specialty, where positions are easier to find in the Unmatch period) would agree to go unmatched. Had their list been exhausted without finding a match, neither candidate would have matched! The NRMP does not, repeat, does not, run each list individually should the combined fail to produce a match.

Febuary 02, 2000