To extend on your edit #1: And, when you go back in time, delete all punishment for murder and see whether you get the same number of murderers.
If you get more than before, the punishment might make some sense in a deterministic world so reinstate it.
Eh, sorry chaos theory doesn't work this way.
It's just as likely you go back and perform whatever magic you need to to delete punishment for murder, then zip back to 'now' and see the world is a global panopticon making sure people don't murder each other.
Some of this may be a failure of people to realize what P !=NP is about, especially in non-linear systems.
Small perturbations in an early state of the system can lead to wildly different outcomes in the final measured state of the system. You can't determine what that will be in non-polynomial time. The only thing you can do is make probabilistic models by running a full simulation in real time (or reality with a time machine I guess).
And it probably does, right? Punishment adds a negative bias to the payoff matrix. Funny side note: increasing punishment severity past a certain point actually saturates and doesn't alter the dynamics further. (which is why modern judicial punishment schedules sometimes seem so mild)