Close-Match 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 min-max, 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.