Ranking Prelim, Advanced, and Categorical

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ns1984

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Quick question...just want to understand the ranking system a little better....

Let's say I am torn between 2 programs, one being an advanced program (which I might like a little better) and the other being categorical. And for simplicity's sake, let's say I've only interviewed at 1 preliminary program, but I really like it. If I wanted to avoid scrambling for a prelim, would I be able to rank the programs as such:

1. Advanced Program + Prelim
2. Categorial Program
3. Advanced Program + Scramble

My guess is no, but I thought I'd see if anyone else has come across this... Thanks for the help!

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Quick question...just want to understand the ranking system a little better....

Let's say I am torn between 2 programs, one being an advanced program (which I might like a little better) and the other being categorical. And for simplicity's sake, let's say I've only interviewed at 1 preliminary program, but I really like it. If I wanted to avoid scrambling for a prelim, would I be able to rank the programs as such:

1. Advanced Program + Prelim
2. Categorial Program
3. Advanced Program + Scramble

My guess is no, but I thought I'd see if anyone else has come across this... Thanks for the help!
Had a similar dilemma a few years ago but it wasn't possible.
 
Had a similar dilemma a few years ago but it wasn't possible.
This is correct.

Once you match into an advanced position, you're taken off the main match list and you go to your supplemental list. So if you matched an advanced program that you listed ahead of the categorical, you would be stuck with that whether you matched prelim or not.
 
This is correct.

Once you match into an advanced position, you're taken off the main match list and you go to your supplemental list. So if you matched an advanced program that you listed ahead of the categorical, you would be stuck with that whether you matched prelim or not.

Does the answer change if you are couples matching? From what I understand, when couples matching, you can list the same program multiple times (that is, you can rank the same advanced program #3, #4, and #8 if you want). However, it's unclear to me whether each rank has its own, individual supplemental list, or if all three ranks use the same supplemental list. If it's the former, it seems like you could rank advanced + prelim > categorical > advanced solo (all with the same program of your partner's), but I'm not sure if that's possible.
 
Does the answer change if you are couples matching? From what I understand, when couples matching, you can list the same program multiple times (that is, you can rank the same advanced program #3, #4, and #8 if you want). However, it's unclear to me whether each rank has its own, individual supplemental list, or if all three ranks use the same supplemental list. If it's the former, it seems like you could rank advanced + prelim > categorical > advanced solo (all with the same program of your partner's), but I'm not sure if that's possible.

It's still the same as if you were matching individually. If you both match your number one couple (Person A - Categorical, Person B - Advanced), that match is locked in and it will choose the intern year with Person B's supplemental ROL for that first choice. If you don't match any of your prelims on that ROL, you are partially matched and have to scramble for an internship. So you either have an ROL ranking prelims in the same city as each Advanced program (higher risk of partially matching), or you can have ROL ranking all your prelims for an Advanced program (good chance of matching but intern year may be somewhere else).
 
It's still the same as if you were matching individually. If you both match your number one couple (Person A - Categorical, Person B - Advanced), that match is locked in and it will choose the intern year with Person B's supplemental ROL for that first choice. If you don't match any of your prelims on that ROL, you are partially matched and have to scramble for an internship. So you either have an ROL ranking prelims in the same city as each Advanced program (higher risk of partially matching), or you can have ROL ranking all your prelims for an Advanced program (good chance of matching but intern year may be somewhere else).

Booooo! That is a bummer!

So basically, if you are worried as to your ability to match into a prelim program, you should rank all categoricals at the top and all advanceds at the bottom. It doesn't seem like it would be that difficult for the NRMP to change the algorithm to allow applicants the flexibility described in OP's hypothetical ROL, but I guess it is simpler not to give people that option.
 
Booooo! That is a bummer!

So basically, if you are worried as to your ability to match into a prelim program, you should rank all categoricals at the top and all advanceds at the bottom. It doesn't seem like it would be that difficult for the NRMP to change the algorithm to allow applicants the flexibility described in OP's hypothetical ROL, but I guess it is simpler not to give people that option.
It would be an even better idea if all of the advanced programs would just go integrated/categorical already. That system is stupid.
 
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Booooo! That is a bummer!

So basically, if you are worried as to your ability to match into a prelim program, you should rank all categoricals at the top and all advanceds at the bottom. It doesn't seem like it would be that difficult for the NRMP to change the algorithm to allow applicants the flexibility described in OP's hypothetical ROL, but I guess it is simpler not to give people that option.

It is probably possible for the NRMP to do this. It assumes that they process Main and Supplemental lists simultaneously, which they probably do. The "problem" is that then applicants would have the potentially unpleasant choice of deciding whether to keep their Advanced spot with SOAPing a prelim, or take a risk of going lower on their rank list and perhaps not matching at all. To avoid that mess, the NRMP would need to allow you to rank the same program twice on your rank list -- once with a supplemental list and once without. That way, you could rank an Avdanced + prelim first, then Cat second, and then the same Adv third but with no prelim. This clearly can be done, but almost certainly a good number of people will "screw it up" and end up worse off. You would need a really good, idiot proof front end to the ranking system to make sure people understood the decisions they were making. And, ultimately, how many people would really benefit from it?
 
It is probably possible for the NRMP to do this. It assumes that they process Main and Supplemental lists simultaneously, which they probably do. The "problem" is that then applicants would have the potentially unpleasant choice of deciding whether to keep their Advanced spot with SOAPing a prelim, or take a risk of going lower on their rank list and perhaps not matching at all. To avoid that mess, the NRMP would need to allow you to rank the same program twice on your rank list -- once with a supplemental list and once without. That way, you could rank an Avdanced + prelim first, then Cat second, and then the same Adv third but with no prelim. This clearly can be done, but almost certainly a good number of people will "screw it up" and end up worse off. You would need a really good, idiot proof front end to the ranking system to make sure people understood the decisions they were making. And, ultimately, how many people would really benefit from it?

yeah, i definitely see what you mean about wanting to avoid that complexity for most applicants.

since couples matching already allows you to rank the same program multiple times at different ranks, i was hoping that this meant you could also submit different supplemental lists with each ranking. technically, i think you can do this. practically, it doesn't seem like it would yield the result you would want, however - if the algorithm locks you into the advanced spot before checking to see if you match on your supplemental list, what's the value of submitting multiple supplemental lists?
 
yeah, i definitely see what you mean about wanting to avoid that complexity for most applicants.

since couples matching already allows you to rank the same program multiple times at different ranks, i was hoping that this meant you could also submit different supplemental lists with each ranking. technically, i think you can do this. practically, it doesn't seem like it would yield the result you would want, however - if the algorithm locks you into the advanced spot before checking to see if you match on your supplemental list, what's the value of submitting multiple supplemental lists?

The value of submitting multiple supplemental lists associated with the same advanced program when you are a couple is that the supplemental list preferences can depend on the partner's program match.

In the following rank list, applicants A and B are willing to commute across the Bay Area for their advanced/categorical programs but would ideally have at least intern year close together.

PartnerA-Advanced -- PartnerB-Categorical -- PartnerA-Supplementals
Rank 1) UCSF Derm -- UCSF Plastic Surgery -- (S1) CPMC Prelim Med, (S2) Santa Clara Valley TY
Rank 2) UCSF Derm -- Stanford Plastic Surgery -- (S1) Santa Clara Valley TY, (S2) CPMC Prelim Med
 
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Agree with above -- allowing applicants to vary their prelim ranks based upon Advanced matches makes lots of sense.

What @littleredwagon is asking for (which is not unreasonable) is the ability to try to match to an Advanced program, then run down the supplemental list, and if you fall off the bottom, then go to the next program on your main list. I.e. if I don't get a prelim for my advanced, I want to try for other programs.

The NRMP would need to create an option at the bottom of the supplemental list "Go to Next Main Rank". if an applicant dropped off the bottom of the supplemental list, then (if selected) the next option on the main list would be attempted, potentially with a new supplemental list if that was advanced. Applicants would have the choice of not selecting that option, and they would keep the advanced match and not match prelim. Then, the NRMP would need to allow applicants to relist any program on their main list again. That way, applicants could choose to match advanced only (and try for a prelim in SOAP), or could list "non-ideal" prelim options as their preference. Rank lists could get really long, and complicated -- a problem itself (the longer lists are, the more likely someone will screw it up).

But, the real problem with this solution is trying to solve the match. In the regular, non-couples match, the solution is completely linear and deterministic. Given the same rank lists from applicants and programs, no matter what order you process the lists in, you'll end up with the exact same solution. And there is only one solution. Once you add couples, and even worse if you were to add flexibility like this, the match rapidly becomes non-linear and may have multiple "best" solutions (i.e. overall "happiness" is the same, but some individuals get better results and some get worse). Without couples, the only way to lose a spot at your #1 rank is for all of the spots to become filled with people ranked above you on the program's rank list. Once that happens, it's impossible for a spot to open up for you. As further lists are processed by the algorithm, the only way someone else gets pushed out is by someone even higher filling a spot. It can never go backwards.

But with the couples match, or with this new proposed option, backsliding can happen. Someone could push you out of a spot (moving you down your rank list), and then end up giving up their spot because they lost the prelim on their supplemental list. You would then want that spot back. That means that the algorithm would need to rework down rank lists that it had already processed. And every time someone gets moved, you have to reprocess all of the lists again. This is easy to do with a computer -- and not even a fancy one. I bet a vanilla windows laptop could process a match like this in seconds. But the interesting problem is that complexities like this probably yield multiple possible final results, and then the NRMP would need to decide which was "best". Not necessarily easy. Would it be better for 5 people to all match to their #2 spot, or 4 people to their #1 spot and one person not match at all?
 
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Thanks, @aProgDirector! I think you definitely understand computational algorithmic processing better than me. This is a little bit of a tangent, but I am curious as to how couples matching (or the "new proposed option") can result in multiple solutions. For instance:

Person A -- Person A's Partner
Rank 1) UCSF -- Stanford
Rank 2) BMC -- Tufts

Let's also say that Stanford only has 2 spots and has the following rank list:
Rank 1) Person A
Rank 2) Person N
Rank 3) Person O
Rank 4) Person P

Let's say that Person A is able to match at UCSF (thus pushing everyone below her one spot - perhaps Persons N and O were BOTH going to match originally, but now, Person O gets kicked off the list.) However, let's say that PersonA's Partner is unable to match at Stanford, so this match is a no go, and Person A is no longer going to UCSF. Before going on to process the next possibility, couldn't the computer essentially do an "undo" maneuver whereby the UCSF list is reset back to its previous state and Person N, O, and P are all bumped back up a spot? If so, it seems like the match should only have one "right" answer.

Looking on Wiki leads me down a mathematical rabbit hole that I don't really understand: https://en.wikipedia.org/wiki/Stable_marriage_problem#Similar_problems. I'm not really sure if rendering a solution NP-complete necessarily means there are now multiple solutions (if there weren't before) or if it just refers to the fact that now the problem is more difficult to solve (or both).

Anyhow, this is all just for my own curiosity now, so if it's too complicated to explain, I guess I will survive not knowing. :)
 
So from what I understand, this appears to be one situation where you SHOULD take into account how much a program likes you while constructing your ROL. If you rank an advanced program #1, you should be confident that at least one of your prelim programs likes you enough that you'll match. Of course, this is probably very easy for the vast majority of people to do, as they most likely have multiple prelim interviews and may not care if the prelim is in a different city.

If, however, you are couples matching and want your prelim to be in the same city, this can actually start to be a situation where you have to do some risk assessment as your supplemental list gets shorter (especially in smaller cities with fewer or just one prelim program). How much you think Michigan's IM program liked you would (and should) strongly influence where you put a Michigan Advanced program on your list. Shooting for your dream program at the top (and getting it) could actually also cause you to go partially matched.

Such is the balance of couples matching, I suppose. I just realized I had realized this earlier before we applied to programs - might have shifted our strategy a bit...
 
So from what I understand, this appears to be one situation where you SHOULD take into account how much a program likes you while constructing your ROL. If you rank an advanced program #1, you should be confident that at least one of your prelim programs likes you enough that you'll match. Of course, this is probably very easy for the vast majority of people to do, as they most likely have multiple prelim interviews and may not care if the prelim is in a different city.

If, however, you are couples matching and want your prelim to be in the same city, this can actually start to be a situation where you have to do some risk assessment as your supplemental list gets shorter (especially in smaller cities with fewer or just one prelim program). How much you think Michigan's IM program liked you would (and should) strongly influence where you put a Michigan Advanced program on your list. Shooting for your dream program at the top (and getting it) could actually also cause you to go partially matched.

Such is the balance of couples matching, I suppose. I just realized I had realized this earlier before we applied to programs - might have shifted our strategy a bit...

I'll respond to this post first, because it's easy. Absolutely yes. If you match advanced in NYC, there are a million prelims and so you have little to worry about. But if you match Advanced at Univ of Iowa, if you don't match there for prelim it's at least 2 hours to the next nearest program. So, you might consider purposely ranking NYC programs higher to avoid that outcome. Unless Univ of Iowa basically promises you a prelim, then you're golden.
 
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Thanks, @aProgDirector! I think you definitely understand computational algorithmic processing better than me. This is a little bit of a tangent, but I am curious as to how couples matching (or the "new proposed option") can result in multiple solutions. For instance:

Person A -- Person A's Partner
Rank 1) UCSF -- Stanford
Rank 2) BMC -- Tufts

Let's also say that Stanford only has 2 spots and has the following rank list:
Rank 1) Person A
Rank 2) Person N
Rank 3) Person O
Rank 4) Person P

Let's say that Person A is able to match at UCSF (thus pushing everyone below her one spot - perhaps Persons N and O were BOTH going to match originally, but now, Person O gets kicked off the list.) However, let's say that PersonA's Partner is unable to match at Stanford, so this match is a no go, and Person A is no longer going to UCSF. Before going on to process the next possibility, couldn't the computer essentially do an "undo" maneuver whereby the UCSF list is reset back to its previous state and Person N, O, and P are all bumped back up a spot? If so, it seems like the match should only have one "right" answer.

Looking on Wiki leads me down a mathematical rabbit hole that I don't really understand: https://en.wikipedia.org/wiki/Stable_marriage_problem#Similar_problems. I'm not really sure if rendering a solution NP-complete necessarily means there are now multiple solutions (if there weren't before) or if it just refers to the fact that now the problem is more difficult to solve (or both).

Anyhow, this is all just for my own curiosity now, so if it's too complicated to explain, I guess I will survive not knowing. :)

Extreme math nerd warning. Do not proceed unless you really like this type of thing.

You were warned!

First, there's no easy way to "just undo" what happened as the match was processing. In your simple example with 4 people, perhaps. But in real life, 100's of other lists might have been processed before Person A gets bumped off Stanford's list because of the couple's match. And, that can have a ripple effect -- whomever is now going to match at Stanford (Person O or P perhaps) may have bumped someone else off of another list, and now that needs to be rolled back, etc. So, ultimately the solution is to continue processing match lists, then wrap back to the begining and look to see if anyone can be moved higher on their list (i.e. looking at all programs higher on the person's list than the place they are currently matched to, are they higher on the program's rank list than the last matched person). If so, match that person at this new program, process the person bumped off down their list (bumping as you go) until someone either fills an unfilled spot or is unmatched. This will leave an open spot at the original person's program. No worries, simply keep processing lists the same way -- ultimately someone will have ranked that program higher than where they matched and will fill that slot. You keep doing this, wrapping around and around all of the lists, until you go all the way around and nothing changes -- that's a stable solution.

Here's the "problem". Most likely, because of the complexity and number of people and spots, there's likely to be several possible solutions. I'll bet that 98% or more is all the same, but 1-2% of people end up in slightly different spots.

Here's a similar example of this: http://forums.studentdoctor.net/threads/match-conundrum.1046918/ In this example, the presence of an applicant who doesn't match can alter the match results. Or, looked at another way, the order the lists are processed can change the match results (in the linked example, if Daniel's list is run last, he doesn't match and the other two end up in their #1's). In the same way, people jumping around into newly opened spots can likely impact the final answer, and making the match more complicated will probably amplify this.

Note that this problem already happens, because of the couple's match. So adding a feature where applicants could choose to "release" their main match if they don't match to a prelim and instead continue working down their main list simply increases the complexity of the problem, but doesn't add a new complexity. And despite looking complicated, I bet a vanilla windows laptop could solve all of this in less than a second. So the main reason NOT to do it is because some subset of people will misunderstand the instructions and end up screwing up their match. The NRMP would need to weigh the benefit of helping some people, with the harm of the people who misunderstand and screw up.
 
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