I am reading the facts and algorithms from very small age. And I am not having such experience .
But @agaddy32 is some how right
As Caspher BFT and Instanbul BFT does works for you but for @agaddy32 query maybe it will not.
I totally agree with @vbuterin your formula but f[n+1] = f[n] * (1 + 0.25 * (w[n] / M — 0.5)) but what I suggest is a semaphore mechanism that will bind the node to particular transaction for f*d but with miner reward of 1/N .Due to majority of miners ledger Blockchain always have some faults .
1.Dependent ledger .I totally agree about miner POS block Production.But the ledger is not stable till majority of them are present , what would it be if majority miner left the ledger ?
2.Making the (virtual critical session) in POS by semaphore(encrpt(private,keyhold)) by miner in ledger will help POS to be better and stable even if majority of miners are not in it . The stabilty of formula will still remains f[n+1] = f[n] * (1 + 0.25 * (w[n] / M — 0.5)) .