Do you feel that the death penalty is justice, or justified vengeance?

I feel that it is the latter because it is using the "eye for an eye" rule. I also add that that rule was made in an age many now consider barbaric and primitive. I find the fact that we are unwillling to forgive those murderers, who we in turn murder, and help them psychologically to be sickening and a stain on human intelligence. Research has shown that the death penalty has done little, if anything, to decrease crime and those unfortunate enough to be executed may end up being acquitted after they have already been executed. To kill another human to avenge the death of another sounds like vengeance, not justice. That is all the death penalty is, state-approved murder. So, to you who feel that all murderers should be executed, why isn't the executioner executed? Didn't he/she kill someone? Are they not a murderer?