I've been thinking about this post on Slate Star Codex for a while, in particular, this part:

Slate Star Codex shows we have no real standard for how potential guilt relates to holding office, except the answer is definitely "some".

Here's my pitch, because this seems like it would minimize frustration in that graph: we use the 51%-ish "preponderance of evidence" standard used in civil litigation. These are all trained lawyers, after all, so it seems thematically appropriate. And we've collectively decided this is appropriate for non-criminal investigations – and I would be astonished if you could allege something more serious than what's already being decided in civil courts.

That's probably also the standard I would use when hiring (and while the public sector is not precisely the same thing, it's still hiring). I could see myself saying, look, he's a really good accountant, and he's probably not a murderer, so leave him alone.

Of course, if the crime is directly related to their job responsibilities (for public office: corruption or misuse of power), I'd probably use a more actuarial calculation – a 10% chance of hiring an accountant with a history of accounting fraud is obviously insanely high.

It's worth taking a moment to think about this, I think, because there are a lot of people making very confident statements, who won't even be humiliated as a hypocrite in the future – their own standards are so unclear you can't hold them to anything. This doesn't diminish the intensity of their feelings, though.