The 4 are always aware of the other 11, because if they werent how could they know what where the majority should be?
And if they started isolated from the main group, for whatever reason?
There are so many ways this can happen, the protocol must be able to recover from this position, otherwise you'll end up like Stellar... frantically searching for a new consensus algorithm while they run one validating node, because they cannot handle forks.
You are very mistaken about how Byzantine agreement consensus works and the requirements needed for a robust one. Bitcoins blocks are not votes, if they were classed and acting as such, then a record would be kept by the network of all votes (orphans). The network doesn't, so they aren't votes, it is a dictation instead.
Blocks
are votes (sybil proof votes at that) in a very real sense. New blocks added to a chain are a vote for that chain, plain and simple. Chains with the most votes win.
The argument that POW is the only solution to the Byzantine problem is ridiculous as it doesn't even meet all the criteria.
In fact, POW is a very robust solution to this problem, able to handle up to 50% byzantine failures, which is the highest I know of. In this thread you state that eMunie is capable of resolving up to (n/3)-1 failures, which is 33%.
Edit: All distributed applications operate as a state machine, Bitcoin's ledger is a state machine also, as is Ripples ledger and everyone elses. If it wasn't a state-machine, then new nodes couldn't download the ledger, replay all the states and end up at the same place as everyone else.
I'm beginning to feel like no matter what argument I present here, even arguments that have been proven by minds smarter than what are behind Bitcoin, they are going to be dismissed just for the sake of arguing.
Quite the contrary - the only reason I'm able to present these counter arguments is that I've been down this theoretical ripple a-like road, in a search for my own fast, energy efficient consensus mechanism. I hope to offer you some food for thought before you go to all that effort of implementation.
You can fix a lot of these problems; here I what I suggest:
* Throw away the trust model completely
* Make votes for transactions cost something (either POW, or burn)
* Handle forks