According to some atheists on this forum, religion should not have ANY decree on murder or killing under any circumstances,
That could be because a lot of people, be they atheist or theist are against capital punishment.
as this proscribes capital punishment and/or provides justification for killing.
Yes.
Some also
disagree with the notion of forgiveness/compensation of crime as an alternative to punishment,
As in making the criminal pay for forgiveness? I doubt a parent, who has had a child murdered, would want to put a price on just how much that child was worth before they granted forgiveness, can you? In some instances, the convicted will be forced to pay compensation and other times, he/she will be imprisoned. And sometimes they may have to do both.
while agreeing that prisons are full of innocent but convicted people.
Yes. There are people who are wrongly convicted.
However, if we look at societies under atheist rulers, they are replete with murder and torture.
Indeed.
Look at Saudi Arabia as an example. Oh wait..
As others have already pointed out in this thread, how many of those "atheist rulers" who ran societies that were apparently "replete with murder and torture", did all of the murdering and torturing in the name of 'atheism' and 'atheist ideals'?
So, in the absence of scriptures and religion, what is the atheists inspiration for murder? What is the "rational" approach to punishment?
So theists need scripture and religion as an inspiration for murder? Now I understand why one theist member, on here, recently said that one should kill if God asks them to kill.
But to answer your (bizarre) question, I simply would not know what inspires one to murder. Some kill out of jealousy, greed, revenge, etc. As an atheist, I have not murdered anyone, to date. I'll be sure to let you know if I am ever 'inspired though'...
As for a '"rational" approach to punishment'? I am not a supporter of capital punishment, but at the end of the day, it depends on the crime involved. Some warrant life imprisonment and others do not.