Match conundrum?

[davesalle]

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I think my friend and I broke the match?

Remi rank list: 1. UIC 2. Mass
Xander rank list: 1. Mass 2. UIC
Daniel rank list: 1. Mass 2. UIC

Mass rank list: 1. Remi 2. Xander 3. Daniel
UIC rank list: 1. Xander 2. Daniel 3. Remi

Mass and UIC each have 1 spot left

So we tried going through the possible scenarios and kept getting stuck. Anyone have a clue as to who would end up matching where? It seems like the student's order of ranking would impact whether they would match or not.

 

[MadHopsMD]

I think Remi goes to UIC, Xander goes to Mass. And Daniel goes unmatched. I think this is the reason the match always favors the candidate.

 

[gutonc]

So we tried going through the possible scenarios and kept getting stuck. Anyone have a clue as to who would end up matching where? It seems like the student's order of ranking would impact whether they would match or not.

Of course the student's order of ranking impacts where they match, that's how it works. The specific scenario you describe is kind of silly (the 2 ranks/application, 1 spot/program) but it could certainly happen.

In this scenario, as MadHops pointed out (while I was in the middle of typing my response), Remi goes to UIC, Xander to Mass and Daniel to Home Depot.

 

[davesalle]

I think Remi goes to UIC, Xander goes to Mass. And Daniel goes unmatched. I think this is the reason the match always favors the candidate.

Whoops just updated it with correct names that makes it an actual conundrum

 

[gutonc]

Whoops just updated it with correct names that makes it an actual conundrum

Same answer. Still not a conundrum. Match favors the applicant.

 

[SouthernSurgeon]

I think my friend and I broke the match?

That's not a conundrum. 3 applicants, 2 spots = 1 unmatched applicant.

I would consider "breaking the match" to mean a scenario where the order in which the algorithm is run changes the outcome (i.e. if Daniel's rank list came up before Remi and Xander and it somehow resulted in him matching).

It seems like the student's order of ranking would impact whether they would match or not.

Of course the student's order of ranking affects the outcome. No one has ever said otherwise.

The point is that (given the program rank lists that you described) there is no scenario in which the order of Daniel's list could have saved him from not matching. Similarly, given those program rank lists, there is no scenario in which the order of Remi or Xander's list could result in them not matching. So as always, the advice given on this site is correct - don't try to "game" the rank list. Rank in order of your preferences.

 

[MadHopsMD]

Of course the student's order of ranking affects the outcome. No one has ever said otherwise.

The point is that (given the program rank lists that you described) there is no scenario in which the order of Daniel's list could have saved him from not matching. Similarly, given those program rank lists, there is no scenario in which the order of Remi or Xander's list could result in them not matching. So as always, the advice given on this site is correct - don't try to "game" the rank list. Rank in order of your preferences.

wait if Daniel put UIC first, would he not have matched?? and Remi gotten screwed?

 

[gutonc]

wait if Daniel put UIC first, would he not have matched?? and Remi gotten screwed?

Nope. In the scenario above, Daniel's not matching no matter what his rank list looks like.

 

[MadHopsMD]

Remi rank list: 1. UIC 2. Mass
Xander rank list: 1. Mass 2. UIC
Daniel rank list: 1. UIC 2, Mass

Mass rank list: 1. Remi 2. Xander 3. Daniel
UIC rank list: 1. Xander 2. Daniel 3. Remi

Mass and UIC each have 1 spot left


Xander gets Mass. ok, because match favors the application. But in this senario why does UIC select Remi over Daniel?

Doent daniel wants UIC and UIC ranked daniel higher then REMI? what am i missing?

 

[gutonc]

Remi rank list: 1. UIC 2. Mass
Xander rank list: 1. Mass 2. UIC
Daniel rank list: 1. UIC 2, Mass

Mass rank list: 1. Remi 2. Xander 3. Daniel
UIC rank list: 1. Xander 2. Daniel 3. Remi

Mass and UIC each have 1 spot left


Xander gets Mass. ok, because match favors the application. But in this senario why does UIC select Remi over Daniel?

Doent daniel wants UIC and UIC ranked daniel higher then REMI? what am i missing?

Because I misread your post. You're correct.

But again, not a conundrum, the match isn't broken.

 

[SouthernSurgeon]

Remi rank list: 1. UIC 2. Mass
Xander rank list: 1. Mass 2. UIC
Daniel rank list: 1. UIC 2, Mass

Mass rank list: 1. Remi 2. Xander 3. Daniel
UIC rank list: 1. Xander 2. Daniel 3. Remi

Mass and UIC each have 1 spot left

Xander gets Mass. ok, because match favors the application. But in this senario why does UIC select Remi over Daniel?

Doent daniel wants UIC and UIC ranked daniel higher then REMI? what am i missing?

I didn't read anyone above me's posts carefully enough apparently. (Or the OP's edits made your initial response incorrect).

In the OP's scenario::

Remi rank list: 1. UIC 2. Mass
Xander rank list: 1. Mass 2. UIC
Daniel rank list: 1. Mass 2. UIC

Mass rank list: 1. Remi 2. Xander 3. Daniel
UIC rank list: 1. Xander 2. Daniel 3. Remi

Mass and UIC each have 1 spot left

Remi would match at Mass. Xander would match at UIC. Daniel would go unmatched. You people have had it backwards since the first reply.

This is the same in your altered scenario in which Daniel ranks UIC #1.

 

[SouthernSurgeon]

If you're not getting it, Just watch the linked video in this post:

The best thing that clArified it for me was the video below.

Anyone who is using the match should watch it, period. Too many students fall into the trap of playing some kind if "game" with their rank order list instead of Just ranking programs in order!

 

[Winged Scapula]

You guys are match nerds.

 

[SouthernSurgeon]

You guys are match nerds.

Fixed that for you.

 

[mvenus929]

Remi rank list: 1. UIC 2. Mass
Xander rank list: 1. Mass 2. UIC
Daniel rank list: 1. UIC 2, Mass

Mass rank list: 1. Remi 2. Xander 3. Daniel
UIC rank list: 1. Xander 2. Daniel 3. Remi

Mass and UIC each have 1 spot left


Xander gets Mass. ok, because match favors the application. But in this senario why does UIC select Remi over Daniel?

Doent daniel wants UIC and UIC ranked daniel higher then REMI? what am i missing?

I think I got it figured out. So Remi prelim matches at UIC. Then we move to Xander, who wants Mass. Because Remi is prelim matched at UIC, Xander gets Mass. Then we move to Daniel. He wants UIC, who ranked him higher than Remi, so Daniel gets prelim matched at UIC, and we go back to Remi. His second choice is Mass, and he is ranked higher there than Xander, so he gets prelim matched at Mass. Then we have to go back to Xander, who would match at UIC because he is ranked higher than Daniel. Then, all the spots are filled, so Daniel doesn't match.

If Mass ranked Xander over Remi, then Xander would have gotten Mass, and Daniel would have gotten UIC, I think.

 

[NotAProgDirector]

Remi rank list: 1. UIC 2. Mass
Xander rank list: 1. Mass 2. UIC
Daniel rank list: 1. UIC 2, Mass
Mass rank list: 1. Remi 2. Xander 3. Daniel
UIC rank list: 1. Xander 2. Daniel 3. Remi
Mass and UIC each have 1 spot left

Reposted so we don't get more confused than we already are

I think I got it figured out. So Remi prelim matches at UIC. Then we move to Xander, who wants Mass. Because Remi is prelim matched at UIC, Xander gets Mass. Then we move to Daniel. He wants UIC, who ranked him higher than Remi, so Daniel gets prelim matched at UIC, and we go back to Remi. His second choice is Mass, and he is ranked higher there than Xander, so he gets prelim matched at Mass. Then we have to go back to Xander, who would match at UIC because he is ranked higher than Daniel. Then, all the spots are filled, so Daniel doesn't match.

This is correct. You'll find that it doesn't matter what order you start processing candidate rank lists -- even if you start with Daniel and end with Remi we should get the same outcome:
1. Daniel #1 prelim match to UIC
2. Xander #1 prelim match to Mass
3. Remi wants #1 UIC, but is ranked below Daniel, so doesn't get it
4. Remi wants #2 Mass, ranked above Xander, so bumps him out, Remi prelim match to Mass
5. Xander wants #2 UIC, is ranked above Daniel, bumps him out, Xander prelim match to UIC
6. Daniel wants #2 Mass, ranked below Remi, so doesn't get it.
7. Daniel is at the end of his rank list, doesn't match.

So, net result is Remi/Mass, Xander/UIC, and Daniel/Unmatched, same as above.

It looks like all is good in the world, right?

OK super match nerds, now watch this: let's say Daniel withdraws from the match. I mean, he's not going to match anyway, right?

See what happens? Why?

 

[Winged Scapula]

 

[Raryn]

Assuming you rank all the programs you interview, there is no possible order that could affect (positively or negatively) *whether* you match. The only thing it can affect is *where* you match. Hence why the only reasonably strategy for someone who cares where they match (i.e. anyone) is to rank the programs in the order in which they prefer them. As the above examples show, there is no way trying to game the match can advantage you.

(Note: Couples match makes things a fair bit more complicated, but the basic rules hold true. If you rank all combinations, the only thing the order changes is where you match. Nothing can affect *whether* an individual, or the couple together, matches except if they simply neglect to rank some of the combinations)

 

[SouthernSurgeon]

Assuming you rank all the programs you interview, there is no possible order that could affect (positively or negatively) *whether* you match. The only thing it can affect is *where* you match. Hence why the only reasonably strategy for someone who cares where they match (i.e. anyone) is to rank the programs in the order in which they prefer them. As the above examples show, there is no way trying to game the match can advantage you.

Yes. And additionally, the only way it affects *where* you match is in the order you prefer (i.e. a lower ranked program can't "jump" your order of preferences unless none of the programs higher on your list rank you highly enough to match there, and ranking a program lower doesn't decrease your chances of matching there unless you match at one of your higher programs)

 

[qmcat]

OK super match nerds, now watch this: let's say Daniel withdraws from the match. I mean, he's not going to match anyway, right?

See what happens? Why?

Then Remi and Xander both get their #1 choice: Remi/UIC, Xander/Mass. Is that right?

 

[NotAProgDirector]

Then Remi and Xander both get their #1 choice: Remi/UIC, Xander/Mass. Is that right?

Yes, exactly. Which appears strange, since Daniel didn't match anyway, it seems as if his withdrawal should have no effect, but it actually reverses the outcome. The question is "why", and is it evidence that the match is "broken".

Of course the match isn't broken.

The reason has to do with the way ties are settled. If Daniel withdraws, we have a "tie" situation. Remi and Xander have chosen two different programs as their #1, and those programs have ranked the opposite person as their #1 pick. So, either Remi and Xander get their 1st choice and the programs get their 2nd choices, or vice versa (programs get their first choice, applicants get their second choice). The match settles all ties in favor of the applicant, hence without Daniel in the match Remi and Xander get their first choices.

But once Daniel's in the match, the system tries to match him as best it can, and doing so ends up settling the tie the other way.

I wonder if the match addresses this issue? They simply would run the match, see who doesn't match, take them out completely, and then re-run the match again. The only problem with this is that if rerunning the match after withdrawing those who don't match the first time generates more people who don't match -- I can't tell if that's possible or not. I think it is NOT possible -- that the only change that can come from re-running the match after withdrawing people who don't match is some group of people switching their matches with each other. But that's an educated guess.

 

[IMPD]

Yes, exactly. Which appears strange, since Daniel didn't match anyway, it seems as if his withdrawal should have no effect, but it actually reverses the outcome. The question is "why", and is it evidence that the match is "broken".

Of course the match isn't broken.

The reason has to do with the way ties are settled. If Daniel withdraws, we have a "tie" situation. Remi and Xander have chosen two different programs as their #1, and those programs have ranked the opposite person as their #1 pick. So, either Remi and Xander get their 1st choice and the programs get their 2nd choices, or vice versa (programs get their first choice, applicants get their second choice). The match settles all ties in favor of the applicant, hence without Daniel in the match Remi and Xander get their first choices.

But once Daniel's in the match, the system tries to match him as best it can, and doing so ends up settling the tie the other way.

I wonder if the match addresses this issue? They simply would run the match, see who doesn't match, take them out completely, and then re-run the match again. The only problem with this is that if rerunning the match after withdrawing those who don't match the first time generates more people who don't match -- I can't tell if that's possible or not. I think it is NOT possible -- that the only change that can come from re-running the match after withdrawing people who don't match is some group of people switching their matches with each other. But that's an educated guess.

If we assume that after validating data, the Match is probably run in a variety of ways to test the final outcome. Again, just guessing, but if I were running it, I'd "run" the Match a few hundred times with minor tweaks to ensure that the optimal outcome had been found.

 

[Raryn]

If we assume that after validating data, the Match is probably run in a variety of ways to test the final outcome. Again, just guessing, but if I were running it, I'd "run" the Match a few hundred times with minor tweaks to ensure that the optimal outcome had been found.

The match algorithim is publicly available, with some papers published in JAMA in the late 90s about all of the math behind it after the last time it was changed. (In the late 90s it was changed to it's absolute "applicant preference first" as opposed to a previous sort-of hybrid system).

I would presume if they made any changes to a sequenced approach such as the one you and APD are proposing, they'd have published papers to that effect as well. My bet is they just run the normal algorithm once and let the results stand on their face.

 

[Fenster]

Fixed that for you.

You beat me to it.

 

[Winged Scapula]

You beat me to it.

By about three weeks! Where've you been?

 

[DoctwoB]

Yes, exactly. Which appears strange, since Daniel didn't match anyway, it seems as if his withdrawal should have no effect, but it actually reverses the outcome. The question is "why", and is it evidence that the match is "broken".

Of course the match isn't broken.

The reason has to do with the way ties are settled. If Daniel withdraws, we have a "tie" situation. Remi and Xander have chosen two different programs as their #1, and those programs have ranked the opposite person as their #1 pick. So, either Remi and Xander get their 1st choice and the programs get their 2nd choices, or vice versa (programs get their first choice, applicants get their second choice). The match settles all ties in favor of the applicant, hence without Daniel in the match Remi and Xander get their first choices.

But once Daniel's in the match, the system tries to match him as best it can, and doing so ends up settling the tie the other way.

I wonder if the match addresses this issue? They simply would run the match, see who doesn't match, take them out completely, and then re-run the match again. The only problem with this is that if rerunning the match after withdrawing those who don't match the first time generates more people who don't match -- I can't tell if that's possible or not. I think it is NOT possible -- that the only change that can come from re-running the match after withdrawing people who don't match is some group of people switching their matches with each other. But that's an educated guess.

Mind = Blown

So basically this means that unless they rerun the match without those that didn't match, A non utility maximizing outcome can be obtained. Scary.
I also am trying to think if re-running could cause people not to match, hard to say.

 

[NotAProgDirector]

Mind = Blown

So basically this means that unless they rerun the match without those that didn't match, A non utility maximizing outcome can be obtained. Scary.
I also am trying to think if re-running could cause people not to match, hard to say.

This type of outcome is very rare. When they compared an applicant-centric match vs a program-centric match for the same data set (the only difference would be ties like the above), the difference in matches was well less than 1%. So, for the most part, this isn't worth worrying about.

I am almost certain that in a "simple match" if they ran the match, then remove everyone who didn't match, and then ran it again to see if anyone gets a better spot, there would be no way that someone would be unmatched the second time. The only thing that could change would be ties, and that would mean that some number of applicants would swap spots. However, the couple's match adds complexity, and definitely could cause someone to not match in a second run. So, overall, fun to think about but almost certain not to happen -- not worth all the extra work, and possible downside of more unmatched applicants.