the only way to know that precondition is for the system to be centralized so that the count of the traitors is known
Yes we know this. And the same applies to Bitcoin's CPU power.
Thus in some sense the problems are equivalent and the thread topic is incorrect (though I still question whether the problems are in fact equivalent). Just as BGP is solvable
conditionally, so is Bitcoin secure
conditionally.
I call it a
condition rather than a
precondition because in some setups it is clear that the former is more useful. For example, a safety control system may specify that it continue to function properly as long as <1/3 of its components fail.