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On another post of mine, someone said that the idea of a qualified candidate is "elusive" because there are always more qualified applicants than open spots in any program. I thought that was a valid point, and I wanted to ask how most programs select candidates once they've met or exceeded the minimum qualifications. I know research interests/match of faculty is a factor, but there still must be more applicants than any given advisor can take on. So once the "pile" is narrowed down to most "qualified" candidates, how are they chosen?

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    For a funded or an unfunded position?
    – user128815
    Commented Sep 19, 2020 at 6:05
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    First come first served, or they got the highest grade compared to the other applicants in X particular subject because it is crucial to the job / discipline applied for.
    – Solar Mike
    Commented Sep 19, 2020 at 6:06
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    @SolarMike Is "first come first served" really common? I thought committees would look for smaller and smaller details until they found one that gave someone an advantage.
    – user39012
    Commented Sep 19, 2020 at 9:24
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    @SolarMike If there is a submission deadline "first come, first serve" is probably even legally problematic.
    – user151413
    Commented Sep 19, 2020 at 10:11
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    On the basis of speculation as you do, one could just as well say "bribes".
    – user151413
    Commented Sep 19, 2020 at 13:07

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Mor Harchol-Balter has written a fantastic detailed description of the graduate admissions process in selective computer science PhD programs in the US, based on her experience at Berkeley, MIT, and CMU. her description is also consistent with my experience at Illinois.

Short version: There are far far too many highly qualified candidates to admit them all. The graduate admissions committee is looking first and foremost for concrete evidence of research potential. Grades and GRE scores are used primarily as filters and only if they are low. You need supportive recommendation letters from reliable sources (preferably expert researchers in your target area, who have a reputation for identifying strong PhD students) that describe your research experience and interests, in technical, personal, and credible detail. Your statement must describe your own research interests, experience, and goals, in technical, personal, and credible detail, and in the idiomatic language of a researcher rather than a student. Your research interests must match those of someone on the faculty who has advising capacity, and you must look more attractive to that faculty member than the dozens of other applicants who want to work with them.

And then you must get lucky.

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    FWIW I think the matching research interests is probably field specific - it's not a major criteria in biology from my experience.
    – user128815
    Commented Sep 20, 2020 at 8:12
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This varies widely by university and by field. I'll list a few possibilities.

In some fields a faculty member has to decide to take the student on as an advisee. Such fields as lab sciences often work like this and the professor may provide grant funding in their "lab" for the student. But such fields also sometimes require that the application process is completely done through the professor, with a student making direct application for a spot in that lab.

In many other fields, a committee will make a decision. There may be some attempt to assure that the student interests align in general with those of the faculty. There may be some situations in which a student is accepted because some faculty member "needs" an advisee for some reason. Or, it is even possible, that a faculty member might pick out an applicant and lobby for their admission.

There might even be some consideration to whether the department is trying to boost some research area and chooses students matched in some way with that.

And, in those places, such as the US, where most doctoral students work as TAs, there might be some consideration given to a person's potential to do a good job with that.

Finally, if there are a lot of highly qualified candidates, it might be that letters of recommendation become more important. People are looking for students who will be successful and not require too much "extra" shepherding.

This isn't a complete list, of course. Committee members will, of course, differ in what they look for.

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For funded positions the uncompetitive applications are removed and the remaining candidates are evaluated subjectively. Every committee will have different criteria, but for stem fields it tends to go strength of letters (including the prestige of the writer - people I've never heard of count a lot less than people I know), strength of current work, and grades might get used as a tiebreaker. Some places might sneak gre scores in somewhere but that's less and less common. The important thing is making sure the people you commit to funding for 5-7 years will not be a huge pain in the ass and will be competitive when they leave for jobs and fellowships.

Unfunded positions tend to just order everyone by gpa gre and prestige of the school they did undergrad. The important thing is filling the class.