It is a known fact that a great many of the people sitting on death row are either mentally handicapped or mentally ill. According to a 1987 report by the Clearinghouse on Georgia Jails and Prisons, 20% of that states death row inmates were either severely mentally handicapped or of below normal intelligence.
This is a problem, because in America insane people arent supposed to be executed. According to the 1986 Supreme Court decision Ford v. Wainwright, a person has to be certified as competent before they could be executed meaning that they had to understand that they were about to be killed and why.
This has lead to some interesting ways of establishing competency (when officials have bothered at all). One of the most ethically challenging was a case in Louisiana where officials forcibly medicated an insane death row inmate in order to kill him. The medication, after all, made him competent enough to die. The fact that he apparently wasnt competent when he committed the crimes didnt seem to matter.
But why is it wrong to execute insane people? Such a prohibition makes sense under the premise of a Christian theological system. After all, if a person isnt mentally competent, then they cannot repent of their sins before they die, meaning that they will go to hell without any prospect of heaven. If, however, they are kept alive, then there will remain at least the possibility of a change which will allow the person to repent. But if you dont believe in souls, there is no moral difference between executing sane and insane people.
For atheists, however, such a consideration simply isnt relevant and it shouldnt be relevant to a justice system which is secular rather than theocratic. As a matter of fact, it is questionable whether or not an atheist can legitimately support capital punishment at all.
For the average theist, imposing the penalty of death can be made to seem less horrible by the fact that it only terminates the body, not the soul. Damnation, not death, is the ultimate penalty and that would be imposed by God, not the state. Indeed, having to face the death penalty may be the path which leads the condemned person to salvation.
This perspective is not something which I am simply making up. Instead, it constituted an important facet of the defense of capital punishment for a long time. But it is not a defense which can be used by secular courts of secular people. Perhaps the most famous explication of this position was made by Albert Camus:
When an atheist or skeptical or agnostic judge inflicts the death penalty on an unbelieving criminal, he is pronouncing a definitive judgment that cannot be reconsidered. He takes his place on the throne of God, without having the same powers and even without believing in God. He kills, in short, because his ancestors believed in eternal life.
A religious person who uses capital punishment does not thereby judge that the condemned person is irredeemable. The atheist who uses capital punishment, however, does make such a determination eliminating someones presence on Earth is effectively the same as stating that rehabilitation and redemption are impossible or just undesirable. But what atheist is competent enough to make such a judgment?