It's a couples match, it's disadvantageous because residencies must now decide they want both of you for you to match there.
Even without disclosing it hurts your odds. Chances of Residency A or B or C (my top 3) ranking me well, vs chances of Residency A or B or C (my top 3) ranking both of us well. Latter will always be lower?
That's simply not true. By listing out every possible combination and ranking them appropriately, you can make the P(A) + P(B) = P(A+B) where A=applicant A matching where they want, B=applicant B matching where they want, and A+B is both applicants couples matching where they want.
Take this toy example where applicant A has three ranks: 1, 2, and 3 and applicant B has 3 ranks, X, Y, and Z.
Set M = all applicant A's options (1, 2, 3, unranked)
Set N = all applicant B's options (X, Y, Z, unranked).
Take the cartesian product of sets M and N to get all possible combinations, but exclude the possibility that both of you go unmatched.
This set is the new set of ranks you have to list, N x M and it is {1X, 1Y, 1Z, 2X, 2Y, 2Z, 3X, 3Y, 3Z, 0X, 0Y, 0Z, 10, 20, 30}
Now, if applicant A's ranking is: 1, 2, 3 in descending order down their rank list and applicant B's ranking is X, Y, Z in descending order down the rank list, it is clear to see the individual ranking opportunities.
You can craft the list of set N x M in such a way as to mimic the case where you matched individually by doing the following:
New rank list:
1. 1X
2. 1Y
3. 1Z
4. 2X
5. 2Y
6. 2Z
7. 3X
8. 3Y
9. 3Z.
10. 0X
11. 0Y
12. 0Z
13. 10
14. 20
15. 30
Think of it like this now: If applicant A had matched individually, he would have either been placed at 1, 2, 3, or gone unmatched, in that order of preference, and applicant B would have done the same at X, Y, Z respectively. This method of numbering ranks as a couple ensures that that same outcome will happen here. If applicant A matches his first choice, applicant B's ranking remains as if applicant B had applied alone (numbers 1->3 of our new list). The same is true if applicant A matched at his second choice (number 4-->6 on our new list), and so on. This method of labeling ensures that
You could also think of it the other way around. If applicant B matches their first choice, applicant A's ranking is still in tact in the list (numbers 1, 4, 7 in our list)
This is only true, however, if you rank all possible combinations of your individual match lists, but if you do do that, your chances of matching in the couples match are identical to that of doing it individually.