I have always regarded the world depicted in the classic Icelandic sagas as analogous to the "Wild West" of North American. The sagas describe the period of settlement (9th through 11th centuries), a time of outlaws and "sword slingers" (as opposed to gunslingers). Every analogy breaks down at some point, but the two periods are reminiscent of one another.

Some in the Libertarian movement have argued that Iceland during the Medieval times had no strong government at all.

According to David Friedman, scholar at UChicago and Milton Friedman's son, Iceland during the medieval period had courts and a legislature. No executive branch of government.

The function of the courts was to deliver verdicts on cases brought to them. That done, the court was finished. If the verdict went against the defendant, it was up to him to pay the assigned punishment--almost always a fine. If he did not, the plaintiff could go to court again and have the defendant declared an outlaw. The killer of an outlaw could not himself be prosecuted for the act; in addition, anyone who gave shelter to an outlaw could be prosecuted for doing so.

Prosecution was up to the victim (or his survivors). If they and the offender agreed on a settlement, the matter was settled.[31] Many cases were settled by arbitration, including the two most serious conflicts that arose prior to the final period of breakdown in the thirteenth century. If the case went to a court, the judgment, in case of conviction, would be a fine to be paid by the defendant to the plaintiff.

In modern law the distinction between civil and criminal law depends on whether prosecution is private or public; in this sense all Icelandic law was civil.

You can find his analysis here. I'll find some other sources and see what I can find on Medieval Iceland.