i think the question is if crime punishment should go as far as death sentence or not, of course in the 2nd case u described a light judgement would be issued (no more than a few years in prison i think). But from what i understand of your post, u agree that some crimes deserve the death sentence.
as for which crimes specifically, that's up for the system to decide; because if all kilers were executed all the same, there wouldnt be really a need for a court trial
