Re: Revenge and justice are very closely related. You'll learn that as you get older.
I don't know why someone downvoted this. I don't know that I'd call the corpus of death-penalty-deterrence-analysis literature "very large", but it's of a decent size (the linked paper reviews some of it). And the paper you linked appears to be a reasonable contribution - I didn't bother checking any of their sources but they discuss methodologies and other issues at some length, and don't seem to be attempting to justify an a priori position.