Ben Laurie at Links.org has written a brief paper about managing consensus between nodes in the Bitcoin network.
The comments on his short paper are far more interesting than the paper itself:
Here’s a great one from Eric Yu, where he discusses the impossibility of someone overpowering the computing power of Bitcoin miners as it relates to our current nation-backed currency system:
The problem with Bitcoin miners not having the majority of the world’s hashing power applies to all national currencies as well (in a slightly different way of course). No country today could resist an invasion by a coalition of the rest of the world, and that coalition could easily abolish its currency. There are many reasons why this doesn’t happen, of course, and a lot of them are relevant to Bitcoin too.
(1) Nobody cares about anyone’s currency enough to go to war about it, (2) Against powerful countries, weaker countries would face a coordination problem – if Nicaragua and Honduras wanted to attack the U.S., they would have a hard time getting anyone to join them, because any coalition with just one more country would still be too weak. With Bitcoin, the equivalent of (1) is that any group that had the resources to do that would gain much more from mining Bitcoins, and (2) probably no single group can out-compute the Bitcoin network right now — it has more computing power than the top 500 supercomputers combined. While your point makes sense, it is unlikely to be a practical problem for Bitcoin, just as a foreign invasion is unlikely to be a problem for the U.S. dollar, the euro, the yuan, etc.
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