CloseMatch Approval Cutoff

This is a concept that just occurred to me now so let me know if it reduces simply to something else, or if there’s an obvious flaw. But the idea is as follows:
 Let voters score candidates independently on some arbitrary scale.
 Determine the score cutoff for approval that minimizes the approval difference between the top two candidates, subject to the constraint that the difference be nonzero if possible.
 Elect the top approved candidate under that cutoff choice.
If voters minmax, this reduces to approval voting. Otherwise it takes some account of differential ratings. There are obviously other ways to take account of them, maybe somebody will have a different idea. One could also minimize the relative approval difference.

I can't see a proof that it is additive. I can't see a proof that it is Frohnmayer balanced. If a system isn't both of those things, I don't know how to convince myself that it accords equal influence to the voters regardless of how many or few candidates the voters oppose. And without equality, I fear that the monied interests can find a strategy within the system to confine the voters to a Prisoner's Dilemma and thereby prevent them from having any effective power over governmental policy.