The Icelandic Commonwealth was in fact incredibly stable for centuries. The reasons it destabilised can be clearly identified:
-- First of all, when Iceland converted to Christianity, the church began to demand tithes. This was the first involuntary payment the people of Iceland ever had to render unto anyone. Payment of a g
oði had been voluntary, and those who refused to pay the typical contribution towards maintaining the legal order of the
goði and the
þing were treated like anyone without insurance in a free market economy: if they needed access to the 'court', they had to pay a fee up front. Such people weren't ordered to buy into the 'insurance': they were simply identified as
niþingers. That is: "no-thingers", "ones who aren't part of the
thing". The introduction of church tithes introdced involuntary payments, and set a seriously dangerous precedent when it came to maintaining the traditional Icelandic system, which had been based (quite literally) on being voluntary. (Keep in mind that Iceland was first settled by people who didn't want to pay taxes to, or obey laws laid down by, a king.)
-- The fuction of "Law-speaker" was also made permanent within a century of Christianisation. At a meeting of the
Alþing, this Law-speaker was authorised to interpret justice (as there was no written law). Previously, such a person was chosen in instances of uncertainty. Now, this position became permanent. This further eroded the initial freedom to interpret justice in a way that the popular assembly saw fit, and concentrated such authority in one person. Binding precedent thus gradually became more important than "case-by-case judgement", turning the extraordinarily free Icelandic system into a far more 'typical' system of predetermined rules. A major problem was that the Law-speaker was paid for his job... by the church. The same church that had inroduced involuntary tithes.
-- Finally, with the tithe revenue, the church sponsored certain key clans, which it bound to itself. Over twe centuries, five powerful families bought up a majority of the 36
goði-titles in Iceland. And there were only allowed to be a fixed number of
goðords. Around 1220 thery obtained the majority, giving them unprecedented and highly dangerous power over the institutes of justice. This also meant far less choice for the people when it came to finding a 'court' for a legal case. More often than not, they were faced with a predjudiced magistrate belonging to a fixed oligarchy. At the end, these wealthy families, backed by the church, introduced taxation to Iceland.
These developments caused armed resistance, and it was this series of disturbances that Haakon IV of Norway exploited to invade. He offered his aid to the established families, and by their leave, he brought an army and subjugated Iceland. Looking at what transpired, we can easily see what ought to be done to preserve Iceland as it was:
-- The rule that there were only allowed to be a fixed number of
goðar should be scrapped. Rather than fixing their territorial reach, as
@Kerney suggested, I would instead simply propose that anyone who wished to call himself
goði and set up a
goðord should be free to do so. If the people trust your judgments, you will get 'customers'. If you are a shit judge, you will soon be out of business. This attitude sounds highly libertarian for today's world, but would not be strange to the people of the Icelandic Commonwealth.
-- The function of "Law-speaker" should not be made permanent, and should only remain an option based on an
ad hoc basis. Furthermore, the office should remain unpaid, and the Law-speaker should certainly not be on the church's payroll.
-- Speaking of the church: tithes should be voluntary. Just as payments to the
goði and the
þing were voluntary, so should payments to the church. Those who didn't pay tithes would simply remain outside the congregation and be refused sacraments and Christian burial. That should be motivation enough. (Observe that Iceland chose to adopt Christianity though what was essentially a referendum. Just have this condition of voluntariness be part of the people's decision. That can be the POD.)