If it is immoral/illegal/what have you for an individual to commit murder, how is it moral/legal/what have you for a group of people to commit murder. Logically inconsistent.
I would require proof that the death penalty "works" before accepting your argument.
Anyhow, this post was about how Democrats (and Republicans) both relabel certain "evils" (in this case murder) to justify carrying them out (protect good people from bad people, or, as you say, deter other bad people from commiting murder).