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