If "deterrence" theories had any validity, the Middle Ages would be remembered as a golden age of peace and civility. Conversely, shouldn't states without the d

If "deterrence" theories had any validity, the Middle Ages would be remembered as a golden age of peace and civility. Conversely, shouldn't states without the death penalty be positively crime ridden compared to the revenge-happy southern states? I'm being somewhat trite, but it doesn't take too many thought experiments and statistical exercises to see that revenge doesn't serve justice.