question about making rank list/match list

[wmd95]

i know this has been said a million times already to rank based on your true preferences and not where you think you have the highest chances. but i think this is under the assumption that you do NOT know how you are being graded, correct?

let's assume you did an away/subI rotation evaluation back at this program and it is average (at best)/not honors AND you feel like you did average/not too good during your interview with the Program Director. Would this change the match strategy?

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[NotAProgDirector]

No.

Your best ranking strategy is ALWAYS to rank programs in the order you want to go, regardless of what you might think they would do.

Let's say you decide to rank this program #1. Let's also assume that they do not rank you at all. In that case, the match will work on placing you at your #2 rank as-if it was your #1 rank.

Put another way -- if you were to compare outcomes of putting a rank list in, vs ranking 10 programs where you didn't apply followed by that same rank list, you will match to exactly the same spot.

You cannot hurt yourself by ranking programs that are longshots high on your list.

If you do not match at all, you would not match no matter what order the list was in.

 

[deleted1095841]

I agree with NotAProgDirector in general, but for the sake of thought, consider the following scenario:

Suppose Alice, Bob, and Caroline are all participating in the match, along with many other students

Suppose Alice is interested most in Program W, followed by programs X, Y, and Z in that order
But she knows that program X and W ranked her very low

Further suppose that program X and W are competitive programs and rank Alice, Bob, and Caroline all very low
And program Y has only 2 slots and ranks 1) Bob, 2) Alice, 3) Caroline
and program Z has only 2 slots and ranks 1) Alice, 2) Bob, 3) Caroline

If Alice ranks: 1) W, 2) X, 3) Y, 4) Z
and Bob ranks 1) Z, 2) Y, 3) some other program, 4) some other program
and Caroline ranks 1) Y, 2) Z, 3) some other program, 4) some other program

Then Alice will match at Z
Bob will match at Y
Caroline will either match at some program lower on her list or not match at all

Alternatively,
If Alice ranks: 1) Y, 2) W, 3) X, 4)Z
and Bob and Caroline make the same choices as before,

Then Alice will match at Y
Bob will match at Z
Caroline will either match at some program lower on her list or not match at all

Notice that by changing her strategy, Alice could match at Y rather than Z

This situation is unlikely to happen to you, and even if it happened, the chance you would know is even lower. But it is a theoretical possibility.

 

[NotAProgDirector]

No, that's not how the match works. Let's look at your first scenario

Alice - W, X, Y, Z
Bob - Z, Y, -, -
Caroline - Y, Z, -, -

All have 2 slots:
W - doesn't rank any of them (or low)
X - Doesn't rank any of them (or low)
y - Bob, Alice, Caroline
Z - Alice, Bob, Caroline

The match will first try to place alice at W and X which doesn't happen, so will prelim place her in Y.
Bob will be placed in Z
Caroline will be placed in Y
... and we will be done.

I'm going to guess that you have a typo in your scenario, and there's only one position per program. In that case, all else being the same:

Alice gets prelim placed in Y
Bob gets Prelim placed in Z
Caroline wants Y also. Looking at Y's list, they want Alice more than Caroline, so Caroline does not get Y
Next Caroline wants Z. Z wants Bob more than Caroline, so Caroline does not get Z
So Caroline will get one of her other programs, or maybe not match at all.
Final result is Alice in Y and Bob in Z.

Let's say the applicants are processed in the reverse order, again 1 slot per program:
Caroline is prelim placed in Y
Bob is prelim placed in Z
Alice can't go to X or W. So next we try to place her in Y. She is ranked above Caroline, so she is placed in Y and Caroline is bumped out.
We try to place Caroline in Z, but Bob is already there and ranked above Caroline. So not an option.
Same result. Alice Y, Bob Z, Caroline something else.

You're welcome to explain why you think Alice will match at Z in your first scenario.

 

[deleted1095841]

No, that's not how the match works. Let's look at your first scenario

Alice - W, X, Y, Z
Bob - Z, Y, -, -
Caroline - Y, Z, -, -

All have 2 slots:
W - doesn't rank any of them (or low)
X - Doesn't rank any of them (or low)
y - Bob, Alice, Caroline
Z - Alice, Bob, Caroline

The match will first try to place alice at W and X which doesn't happen, so will prelim place her in Y.
Bob will be placed in Z
Caroline will be placed in Y
... and we will be done.

I'm going to guess that you have a typo in your scenario, and there's only one position per program. In that case, all else being the same:

Alice gets prelim placed in Y
Bob gets Prelim placed in Z
Caroline wants Y also. Looking at Y's list, they want Alice more than Caroline, so Caroline does not get Y
Next Caroline wants Z. Z wants Bob more than Caroline, so Caroline does not get Z
So Caroline will get one of her other programs, or maybe not match at all.
Final result is Alice in Y and Bob in Z.

Let's say the applicants are processed in the reverse order, again 1 slot per program:
Caroline is prelim placed in Y
Bob is prelim placed in Z
Alice can't go to X or W. So next we try to place her in Y. She is ranked above Caroline, so she is placed in Y and Caroline is bumped out.
We try to place Caroline in Z, but Bob is already there and ranked above Caroline. So not an option.
Same result. Alice Y, Bob Z, Caroline something else.

You're welcome to explain why you think Alice will match at Z in your first scenario.

Thanks for considering!
You're right - I meant to say each program has one slot.

But why doesn't Bob get prelim placed in Y? (Since Y put Bob at #1)

Suppose W and X are processed first. Neither of them want any of our students.
Then Y picks Bob for now (until they find a better student, which will never happen, since they like Bob the best)
Then Z is processed and they pick Alice for now
Z is happy with Alice, so they're not going to try to get Bob

Maybe I'm not understanding it right?

 

[NotAProgDirector]

I see the confusion.

The match is "applicant proposing". So it works from applicant lists first, using program lists to resolve conflicts.

So Bob never gets prelim placed in Y, because the match works off of his list and places him in Z. And since the only person that Z wants more than Bob is Alice, and Alice wants Y before Z, it's never an issue.

What you're (perhaps) getting at is that for programs, there can theoretically be a benefit to shortening rank lists. So, let's say in this example that programs Y and Z decide not to rank Alice and bob respectively. So now program rank lists look like this:

W - doesn't rank any of them (or low)
X - Doesn't rank any of them (or low)
y - Bob, Alice, Caroline
Z - Alice, Bob, Caroline

Now what happens is this:

For Alice, we try W and X without success. Now Y is without success also, so Alice gets prelim matched to Z
Bob we try for Z but that's not an option, so Bob prelim match to Y
Caroline still out of luck, tries for Y and Z but she is ranked below Bob and Alice so she will end up somewhere else.

This yields your Alice - Z, Bob - Y solution.

What's happened here? Because the match is applicant-proposing, ties are broken in favor of the applicant. We can see that in Bob/Alice. Alice wants Y over Z, and Bob wants Z over Y. The programs have the exact opposite choices. So the match will follow the applicant preferences. But, theoretically, programs can force the tie to break their way by not ranking the student. If they "rank them very low" then it's no longer a tie, since the program prefers other applicants.

Although interesting mathematically, it's completely meaningless in real life. Less than 1% of the match are these ties, so trying to game the system is stupid. And, although a program could theoretically break a tie in their favor, this type of strategy (shortening rank lists) will greatly increase their risk of not filling at all. And, the honest truth is that if two candidates are next to each other on a program list, we don't really care which one we get.

Your issue would exist if the match was program-proposing. It's the same issue the other way round.

 

[Captain_Falcon]

And, the honest truth is that if two candidates are next to each other on a program list, we don't really care which one we get

At what point on a rank list does the program really begin to care who they don’t get and who they end up with?

 

[NotAProgDirector]

Your question is unanswerable. Each program will be different. My point was simply that when you rank large numbers of candidates, the differences between them become small.

 

[havil]

No.

Your best ranking strategy is ALWAYS to rank programs in the order you want to go, regardless of what you might think they would do.

Let's say you decide to rank this program #1. Let's also assume that they do not rank you at all. In that case, the match will work on placing you at your #2 rank as-if it was your #1 rank.

Put another way -- if you were to compare outcomes of putting a rank list in, vs ranking 10 programs where you didn't apply followed by that same rank list, you will match to exactly the same spot.

You cannot hurt yourself by ranking programs that are longshots high on your list.

If you do not match at all, you would not match no matter what order the list was in.

hey mind if I DM you? I have a question

 

[NotAProgDirector]

Sure, go right ahead