Oh hey look, it's around midnight here and I'm on a posting spree, what harm could I possibly cause?
Anyways as much as I have had experience with voting there's 2 sensible things that could be done(or atleast right now I can imagine 2).
1) You could have the moderators vote as was suggested by Drakon, but that would only work if you first got rid of the "undeserving people". Then the general opinion of the masses would be viewed by the administrators who would also make the final decision(acting as tiebreakers when necessary).
2) The other possibility is to have people(of whatever rank you choose and up) simply share their opinion about said applicant. Then the administrator(s) would decide the fate of the apply, taking into consideration what was said by the others. The only difference from the 1st option would be that the moderators/VIPs/whatever could simply say what they think, they wouldn't necessarily make a difference by themselves.
Hope you guys got what I meant. I am sleepy and my brain is slowly ceasing to function...