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