I was in an Amnesty International group for a long time. I still consider myself involved though I'm not going to meetings.... and er, haven't written an Urgent Action in a while. But you never de-Amnesty.
We discussed the death penalty quite a bit and one of the obvious arguments against it is that we have sometimes posthumously acquitted someone on the basis of DNA evidence. We have not been correct 100% of the time. And this leads you to one of two conclusions. (1) Even one person wrongly killed is too many. It taints the whole death penalty. Or (2) Humans are imperfect and there are going to be mistakes in how a government policy is carried out. The death penalty is valuable to society because the true positives outweigh the false positives. The benefits we get - deterrence, preventing that individual from more crime, vengeance for victims' families - outweighs the harm to the false positives and false positives' familiies.
If you go with option (2), who decides how many false positives is OK and how?
The system of representative government makes sense for a lot of things. As mistakes, mistaken thinking, wrong-headed policy, are represented in the minds of members of Congress, well, it may not be awesome but it is optimal. Members of Congress are just people, and they will/should reflect the presence of mistakes, mistaken thinking, wrong-headed policy ideas, in the electorate overall, in a proportional fashion. This is fine for most issues with checks and balances and recourse, but you cannot ever bring back the victim of false execution. So should there be a different bar set? We're at Shirley Jackson's "The Lottery".