Rejecting graduate school offer while recommending classmate - can this be appropriate?

Question

I am an undergraduate at a U.S. university with a top-10 graduate program in mathematics. I applied to mathematics PhD programs this year, and was lucky enough to get quite a few offers at good places.

Because of the COVID-related cuts, many of my classmates were not so lucky. One of my classmates in particular has very similar interests and background to me, but hasn't heard back from any programs, which (to my understanding) means he is on the waitlist. In fact, we had a letter of recommendation in common, which was based on a document we wrote jointly (the professor who wrote it could not have made any real comparison between our contributions to the document, but he is very famous and the letter is likely very strong).

I know him very well, and I know that his background and competence in our field is equivalent to mine (and actually a lot better in some areas). I will have to reject many offers at places that he hasn't heard back from. When I do so, is it at all appropriate for me to politely indicate my opinion that my classmate would actually be a better fit than me for the program? Would this have any (however small) chance of changing the outcome in his favor? Or is it the case that admissions committees would find this annoying and actually be swayed in the opposite direction?

Maybe this sounds like a strange question, but the reason I ask is that both of us have been studying mathematics very seriously for our entire undergraduate education. We would both be really sad if one of us could not continue in math, so I want to do everything I can to help.

Answer 1

Typically around now in the US, graduate programs will be finalizing their lists for offers of admission and a waitlist. I know for the program I attended for grad school, they ordinarily offered about 50% more slots than they actually intended to admit, knowing that some would choose other offers. If fewer students matriculated than expected, offers would start to go to people on the waitlist.

Other programs, especially those with less funding flexibility, may only admit to the number of slots they have and then grab from the waitlist only when people reject the offer.

It seems very unlikely to me that your slot would go to this student if they have not already been informed they are on a waitlist. It is even less unlikely that your opinion will sway the decision, the admissions committee has already met and reviewed the background of all their applicants. I doubt it would cause any harm, either: the decisions are already made. Whoever read your request might find it a bit of a sweet gesture while being quite naïve, but that's it.

Probably the best thing you can do for your friend is to compare applications to help them prepare for next year's admissions cycle. Maybe there is something in your applications that stands out that they haven't touted as well.