Death Penalty for Child Abusers?

In response to the question, "Should the death penalty be an option for pedophiles and those who kill children?" I recently wrote:

In the millennia of human history, violence for violence has never decreased violence. Of course child abusers, rapists, murderers, elder abusers, animal abusers (pick a reprehensible behavior) should be held accountable, but state sanctioned murder won't fix the problems (nor give the state the moral authority to tackle them). Capital punishment feels good to our primitive impulses, but has never solved any social problem and never will.