Part of my post was to suggest that the data regarding connections between economic diversity and democracy aren't good. The argument that single-product economies aren't democratic is driven almost entirely by the data of Arab oil producing states. So one might as easily make the argument that being Arab or producing oil is the issue, not the economic concentration.

History is much more instructive here. The full story of Iraq seems to be that oil production grew up under semi-colonial rule. The Hashemite monarchy permitted foreign companies to loot the country - taking the oil almost free -- in return for, essentially, kickbacks to the royal family. The Baathists (who are nationalistic socialists, which should ring a bell with some) united a burgeoning middle class and poorer Arabs with a "spread the wealth" program. They proposed nationalizing the oil companies and, secretly, taking much more revenue for the few power-hungry men at the top. But they also spread around a lot more, particularly to the Sunni community, earning their loyalty. In the 1970s, Saddam Hussein consolidated power, relying increasingly on state-run oil (nationalized 1972) to run his government. In the 1980s, export and trade for arms (from the US mainly) became crucial. In the 1990s, sanctions distorted everything. This isn't a story about lack of economic diversity, is it? It's a story of bad Hashemite government.

Alaska demonstrates that even a heavily oil-based economy can work well if the government (essentially) heavily taxes private oil companies and spreads the wealth around. Alaska has no income tax; it's all oil revenue, plus distributions to each citizen each year. The fact that it's not independent isn't that relevant to the point that oil doesn't make them corrupt - or the corruption there is not corrosive.

p.s. - hands off Nauru.