Hoo boy! This SO wrong!
Iceland didnt become subject to Norway until the 14th century, iirc, after 400+ years of independence.
Iceland was settled by farmers in small groups, not organized by 'nobility', so why on earth would they WANT to impose an aristocracy upon themselves. Sure, there were 36, later 39, godhar (singular godhi, alternately translateable a chieftain or priest), but these were more the most important local farmers who had a following than a real aristocracy.
So, basically, ??????