Thanks for clarifying - I would agree that interview selection isn't random overall. I'm just not sure if they put the people they like the most in the first interviews because I don't really see the point of it if they're just going to wait until April to get an answer? Although other schools do do this (like Tufts), so I suppose it's not entirely out of the realm of possibilities, Penn has just never overtly come out and said that they do this.
It would make more sense (ok at least in my head it does) that they select 280-300 people that they feel would be successful at Penn, then interview them randomly because at the end of the day, when they are accepted doesn't matter as they have until Decision Day to commit and they seem to accept the same amount of people during each round of interviews. Unfortunately, they remain very tight-lipped (at least to us) about how they select the order in which they interview candidates.
Ultimately I think trying to pick apart Penn's (as well as other school's) admissions process and how they select candidates can cause unnecessary stress for everyone. We all do it, I certainly did it last year, I'm not trying to be hypocritical here! As long as you (directed at the collective applicants, not you personally) submitted the best application you could with the opportunities you had and did your best as far as academics, experiences, research, LORs, personal statements, etc. you have just as much of a shot as the next person. Unfortunately it seems the application pool is only getting more and more competitive, and it's so easy (especially on forums like this) to compare yourself to everyone else, so I understand how it can be disheartening and frustrating for everyone waiting on interviews and acceptances. Especially when schools like Penn aren't consistent on times and days they send out their interviews and are very ambiguous when you ask for more information.
I'm sorry to hear it's been a rough cycle - hopefully it will get better! If you need anything or just need to vent, my inbox, as well as the inbox of many others on here, is open. This is a great community to have support you as we all have different experiences and different paths to getting into vet school. No matter what, I know you'll get there and I know you'll be a great doctor!