There have been several proposals for how we’re ever going to get a handle on the ever-mounting close-vote queue. Dupehammer has been especially successful, and there have been several proposals since Mjölnir for awarding more close votes one way or the other, including one to give extra close votes, only accessible via /review and one to have a closehammer.
Here is a simple proposal to grant more close votes without any fancy logic.
We should make close votes scale the way delete votes scale. Currently, you are granted 5 delete votes with the privilege, and then 1 more per 1,000 reps up to a maximum of 30 per UTC day.
With close votes, upon reaching the privilege you are granted 24 on most sites and 50 on large sites. But then—nada.
I propose that close votes be made to scale the same way that delete votes do. Your initial award should be same as the current one (24 or 50), but then you would be granted another close vote for every 1,000 reps past that.
Providing for voter fatigue
This sliding daily maximum should probably top out at some reasonable maximum so that Jon Skeet doesn’t end up spending all his time close voting instead of answering. We’d never get to 100,000,000 answers that way.
But to what maximum? More than it is now, perhaps 50 for sites getting below 50 questions per day on average or 100 for those getting above that.
See, I don't know for sure that it makes sense to have a different maximum for large sites than for small sites. Even though I'm sure the 24/50 split must have been triggered by something, I wonder whether it would be good enough just having more close voters as a large site would and have the maximum be the same everywhere, whatever that number is.
Don't worry about the details
The proposed figures given above are all just wags; it doesn't exactly matter what they all are. Maybe the initial award should be 20, or maybe the max by 100 and 200, or 40 and 80. That doesn’t matter. The important idea is that this be made something which scales with rep.
Something vaguely like this has been proposed before, but only in an answer and only roughly. That suggestion was “chunkier”, and had no upper limit for Trusted Users. This one is more fine-tuned to smaller steps, the way delete-votes work.