I'm surprised there are as many supporters of the death penalty here as there are. A couple points.
1) It costs more. That's a fact. Should it? That's a different point. If you think that the appeals process is too long, then there's that, but its a different argument.
2) Is it a deterrent? There's 2 arguments here, scientific and rational. The scientific argument has correlations like the one Tin showed, or other correlations like the fact that states without death penalties have lower murder rates, or....you can look at the rest of the first world. But it doesn't matter, because, and this is a secret so I'll say it quietly CORRELATION DOES NOT SHOW CAUSATION. If you don't understand that then please just GTFO and let the grownups talk. The sad fact is that you are not going to be able to show anything other than correlations with this argument (in either direction), and you are going to have a very hard time convincing anyone of a cause and effect relationship.
The second part, the rational part, where we say "if they see that people are(n't) being put to death for committing murders then they will be (dis)inclined to commit more murders". It makes sense. To a rational person. To bad people that commit first degree murders aren't always rational. A crime of passion is one thing, but to methodically plan and kill a person, that's different. That takes a mindset that very few people have. Cop Killers are another thing as people don't usually plan to kill a cop, it happens in the moment. Its actually the only place I do agree with the death penalty, as there needs to be punitive protection for our boys in blue.
Either way, the rational argument rests on some very shaky ground; it assumes to know the mind of a killer.
3) What if it's thought of as a purely punitive action? Well, then there's no argument against that. It's a moral determination, and can only be countered by a different set of morals. Which means there is no middle ground.
4) Do some people simply not deserve to live? On a moral stance, I find it hard to make that statement, but there are other viewpoints that are equally as valid (the beauty of morality is that it is fluid.) On a societal/utilitarian stance (for the good of all), I believe it's fair to argue that removing them from society is all that matters. Once they are removed from society, they are no longer a threat. Assuming that point 2 is considered to be up in the air, and point 3 doesn't have a significant societal impact (victims families not getting vengeance doesn't cause societal unrest).
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I guess my point is, at the end of the day there is only one point that isn't subjective or unprovable, and that is that it costs more. So, guess where I stand.