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The Carms Algorithm


W0lfgang

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Consider this post-interview rank order list scenario...

 

Toronto ranked:

1.  Tom

2.  Harry

 

Tom ranked:

1.  some school

2.  some school

3.  some school

4.  some school

5.  some school

6.  Toronto

 

Harry ranked:

1.  Toronto

2.  some school

3.  some school

4.  some school

 

It turns out Tom's top five ranked schools didn't rank him and only Toronto liked him, but he liked Toronto the least.  Harry, on the other hand, would love to go to Toronto and ranked them first, but Toronto ranked Tom higher.

 

Does Harry match to Toronto over Tom?

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No, Tom goes to Toronto.

 

The applicant has priority in the algorithm over the school. Meaning if another school (say one that Tom ranked 11th) ranked Tom higher than Toronto (say Tom was #2 and Harry was #3 at Toronto) Tom's choice of Toronto over the other school has priority.

 

People get confused thinking that the choices of the candidates affect each other. In a sense they do but not how you think they do. It doesn't matter how bad Harry wants Toronto, they ranked Tom higher so he has "first refusal". No other school chose him so he gets his best choice which just happens to be 7th on his list. If Tom would have ranked Toronto 8th and the other school that wanted him 7th than Harry would be going to Toronto but as far as CaRMs goes Tom gets his best choice given the other schools not ranking him and Toronto gets their top choice of candidate. Just because Harry ranked them higher does not negate Toronto's and Tom's match priority. 

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No, Tom goes to Toronto.

 

The applicant has priority in the algorithm over the school. Meaning if another school (say one that Tom ranked 11th) ranked Tom higher than Toronto (say Tom was #2 and Harry was #3 at Toronto) Tom's choice of Toronto over the other school has priority.

 

People get confused thinking that the choices of the candidates affect each other. In a sense they do but not how you think they do. It doesn't matter how bad Harry wants Toronto, they ranked Tom higher so he has "first refusal". No other school chose him so he gets his best choice which just happens to be 7th on his list. If Tom would have ranked Toronto 8th and the other school that wanted him 7th than Harry would be going to Toronto but as far as CaRMs goes Tom gets his best choice given the other schools not ranking him and Toronto gets their top choice of candidate. Just because Harry ranked them higher does not negate Toronto's and Tom's match priority. 

 

Indeed, this means that there is absolutely no reason for you to rank a school you do not like higher simply because you feel that the chances are better.  In this case, it did not matter where Tom ranked Toronto: he was not going to go unmatched, regardless of where he ranked Toronto. 

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We are imgs applying both with pr status decent ee and nah scores and good lors from electives in Toronto.

Last yr we couples matched but as I hadn't pr in time both were cut.

This yr I think we should just apply individually to Mac u of T Ottawa and London but herself wants to couples match again. Any comments? Couples match may be too hard for us to get. And if we match say Mac and u of T we have an option of commute and even transfer in 1 year...

Comments?

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We are imgs applying both with pr status decent ee and nah scores and good lors from electives in Toronto.

Last yr we couples matched but as I hadn't pr in time both were cut.

This yr I think we should just apply individually to Mac u of T Ottawa and London but herself wants to couples match again. Any comments? Couples match may be too hard for us to get. And if we match say Mac and u of T we have an option of commute and even transfer in 1 year...

Comments?

 

There is no disadvantage to doing a couples match if you set up your rank order list correctly. If you list every acceptable combination of results for the both of you, including combinations that would result in only one of you matching, you can give yourself the exact same chance of matching to anything as you would with both of you in the individual match, while increasing your odds of matching to the same place.

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I cannot say this enough - the carms algorithm works in a way that in all cases the OPTIMAL SOLUTION is to pick in exact order your preferences. Period.

 

If you have a background in math or economics you can actually prove that formally - flat out prove it. It is based on game theory and standard material in advanced economics classes (actually one of my degrees is in that).

 

When people try to do anything different that is when they set themselves up for failure. So don't do that. If ideal for instance for you to couple match then do that (both at the same place), but if you would also rather match separately than go unmatched as well then rank as couples at the same place first, and then rank all the separate combinations (one at TO and the other at Mac etc). You will not be disadvantaged in any way by doing that. That is just how the system works.

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No, Tom goes to Toronto.

 

The applicant has priority in the algorithm over the school. Meaning if another school (say one that Tom ranked 11th) ranked Tom higher than Toronto (say Tom was #2 and Harry was #3 at Toronto) Tom's choice of Toronto over the other school has priority.

 

People get confused thinking that the choices of the candidates affect each other. In a sense they do but not how you think they do. It doesn't matter how bad Harry wants Toronto, they ranked Tom higher so he has "first refusal". No other school chose him so he gets his best choice which just happens to be 7th on his list. If Tom would have ranked Toronto 8th and the other school that wanted him 7th than Harry would be going to Toronto but as far as CaRMs goes Tom gets his best choice given the other schools not ranking him and Toronto gets their top choice of candidate. Just because Harry ranked them higher does not negate Toronto's and Tom's match priority. 

 

Well said Fry.  It astounds me how many people have complete misunderstanding of the carms algorithm.

 

I have heard of the line of thinking where if you thought your chances at a certain program are low and you rank that program first, you'd be 'throwing your first choice away.' lol

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Well said Fry.  It astounds me how many people have complete misunderstanding of the carms algorithm.

 

I have heard of the line of thinking where if you thought your chances at a certain program are low and you rank that program first, you'd be 'throwing your first choice away.' lol

 

yeah you hear that from time to time - completely the opposite actually of how the algorithm works. 

 

in defense of it we don't spend a lot of time really explaining how it works. Which is fine if you just trust that it works the way we say it does and go accordingly (rank things in order of your preference regardless of what you think that school will do). If you decide you don't trust that (fair enough) then you then really should learn how it works (ha, to learn why you should trust the algorithm actually). 

 

but to ignore the advice of how it works and then blindly make up your own approach? Bad idea. 

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I guess the only way for this to affect you as an applicant is when Tom makes it known to the interviewer that Toronto is undesirable on his list, who would rank him lower than Harry. But still, the best thing to do from school's perspective is also to rank applicants in order of their preference because they should want the best available candidates and keeping the order as is (Tom over Harry for Toronto) would not reduce their chances of getting Harry. 

 

Just my 2 cents, I think I am probably overthinking this already.

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I guess the only way for this to affect you as an applicant is when Tom makes it known to the interviewer that Toronto is undesirable on his list, who would rank him lower than Harry. But still, the best thing to do from school's perspective is also to rank applicants in order of their preference because they should want the best available candidates and keeping the order as is (Tom over Harry for Toronto) would not reduce their chances of getting Harry. 

 

Just my 2 cents, I think I am probably overthinking this already.

 

yeah it is the same for the schools - regardless of what you say they should also rank the applicants in order as well. Doesn't matter what the applicant says they are ranking. That is a completely meaningless statement in the process. 

 

same if the school says they are going to rank you highly. That just doesn't matter - even if completely true. With the algorithm that is completely irrelevant. 

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No one ever asked me what order I was ranking schools, pretty sure this is a no-no question anyway. Being on the other side of it now I can definitely say that schools just rank their top choices, there is no consideration as to what the candidate might rank.

 

Been giving talks on CaRMs and coaching people through it for a couple years now and it really is this simple: rank your choices in the order that you want them whether you are the school or candidate. That is it, that is all, the algorithm takes care of the rest.

 

Where I think people get confused is trying to figure out how they fit into the match with everyone else. There is no way to "game" the system through your choices, the only potential way to affect the match in any way is to get other people to change their rank order.

 

IE: Harry needs to convince Tom to rank a different school (one that accepted Tom) higher than Toronto so that Harry will get the spot that would have gone to Tom if he had not chosen the other school. 

 

Doing this in real life is virtually impossible unless you are the pied-piper or a manipulative puppet master.

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I guess the only way for this to affect you as an applicant is when Tom makes it known to the interviewer that Toronto is undesirable on his list, who would rank him lower than Harry. But still, the best thing to do from school's perspective is also to rank applicants in order of their preference because they should want the best available candidates and keeping the order as is (Tom over Harry for Toronto) would not reduce their chances of getting Harry. 

 

Just my 2 cents, I think I am probably overthinking this already.

 

I have never heard a candidate outright telling a program they were interviewing at that they 'had no interest in being in their program'. 

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I guess the only way for this to affect you as an applicant is when Tom makes it known to the interviewer that Toronto is undesirable on his list, who would rank him lower than Harry. But still, the best thing to do from school's perspective is also to rank applicants in order of their preference because they should want the best available candidates and keeping the order as is (Tom over Harry for Toronto) would not reduce their chances of getting Harry. 

 

Just my 2 cents, I think I am probably overthinking this already.

 

probably overthinking :) If an candidate made it clear they would rank a school lower that would only matter if the school thought that because the residency wouldn't want to be there that having them would case problems. They would then rank them lower because they thought as a result they were not good for there program (rather than directly because the student wasn't going to rank them highly).

 

there are schools that know they will probably be ranked lower - Winnipeg for radiology for instance probably knows they are not going to be at the top of everyone's list. They still rank people in order etc. 

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