I'd argue that even if it's magically determined with 100% accuracy, we still shouldn't give the state the power to decide to kill them. It's unnecessary. Studies have shown that the harshness of the penalty is much less of a deterrent than the certainty of being caught, putting incorrigible sociopaths away in prisons or mental institutions for life is just as effective at both deterring and protecting.

The key is having a trustworthy justice system. If you don't have a trustworthy justice system then no amount of harshness helps, in fact it only hurts.