I mostly agree with your post but, well, I think that private enforcement of law in Medieval Iceland is an example of exactly why we need the state to enforce criminal laws. Have you ever taken a look at NjÃ¡ll’s Saga? (Which the paper you link to cites.) It’s a great read but it tells the (probably largely true) story of an out-of-control feud that results in the murder of something like five percent of Iceland’s male population over a 30 year period. One of the major characters (the Nijal of the common title) is actually a lawyer within the largely private system. And, for his trouble and enormous skill at law he gets burnt alive in a revenge killing. I actually first read it myself in a class on Medieval law.