[mathattack]

There are two ideas.

One thought is that you can back out of a mistake on a very long prison case. You can't back out of the mistake once someone is dead. So let's say you're 99.9% sure someone molested a bunch of kids. You can sign them up for life in prison on those odds. But you shouldn't do it for life, because there's a chance that you're wrong. Please don't ask what the right % is, as I don't know that #. But I do accept that we can never be 100% of any crime. (Is the prosecutor corrupt? Was the suspect mentally ill and not really confessing?) But that doesn't mean we don't punish crime at all. It means we need to have a method of redressing mistakes, which we lose in capital punishment cases.

There's a separate economic argument that just says it's not economic to go through the hassle of it, but this is not a moral arguement.