Do Top Grad Schools Admit Applicants from Less Selective Colleges?

<p>So what do the top grad schools think of good programs at schools with no prestige?
The specific program in question is Michigan State’s James Madison College, a residential college for public policy/poli-sci with smaller class sizes, etc. within MSU (huge school thats not very selective)
With poli-sci and international relations being such large fields, I would imagine there are a ton of applicants to Ph.D programs in the field, so do you think I would be better off trying to transfer into a school with more national name recognition? (Getting into UMich from MSU is supposed to be fairly easy)
I’m not sure how important research is within Poli-sci or International Relations or how abundant it is at the undergrad level, anyone have any insight into this?</p>