I like the idea from the powerball revolution epsiode of Revisionist History (http://revisionisthistory.com/episodes/44-the-powerball-revo...). Why not have some filter to get the top students in to a pool, then randomly select them? I mean there are more qualified students than there are slots, so it's only "fair" if each of them get the same chance. No politics - just a pure number game at that point. You can argue the filter could create a disadvantage to poor students etc..., but you can adjust that in ways that the initial pool of potential applicants will be even.
Of course when I mention the concept of randomly selecting a candidate, it makes people real uncomfortable :)