(disclaimer: Bitcoin is still the best effort that exists at creating a decentralized currency and no altcoin has made a better method.)

I feel this topic deserves it's own thread and would get stonewalled with popular opinion somewhere in the Bitcoin section.  My argument here is:

you can't solve byzantine generals problem with a probabilistic model unless you've first solved sybil with a probabilistic model and Bitcoin doesn't do that
because there's no way of telling if all pools are owned by the same person, then it's not collusion or 51% attack, it's a sybil attack
since the essence of the byzantine generals problem is sybil attack, dealing with sybil comes first in the hierarchy before byzantine generals is discussed at all

The Byzantine problem deals with a minority of actors or signal throwing off the consensus of the system or majority.  If you can't determine how many actors even exist in the first place, you're probably always going to lose this test.  This fact might give credence to some form of deterministic block validators model, but that's outside the scope of this post.

The part where the biggest disagreement will come from, is that people will claim there are incentives against a big hash man owning several pools that make up the majority of hash rate.  This is obviously false.  There are no incentives against him taking this course of action, since he can do so in secrecy, there are only incentives against him making double spends.  I would argue that even if he isn't double spending the security model is broken.  If you accept this security model, there's no reason to not accept a security model of one guy always having 90% hashrate out in the open (not trustless, they can double spend at any time).

How this argument began: