The equation to solve that problem is the following:
The system can tolerate at most of F faulty nodes in a N validator nodes network, where N = 3F + 1
You can visit this link https://github.com/ethereum/EIPs/issues/650 in Consensus part to more information.
A node that is not party to a private transaction can still mine (mint) the transaction. The minting node is selected by whichever consensus mechanism you have configured.
A simplified description of how private transactions work is as follows:
Node A sends the transaction to its local transaction manager and is
returned a hash to the transaction. The ...
To reach consensus w IBFT in the presence of F s faulty nodes require N > 3F validator nodes, or N=3F+1. So to Nathan's original question, the total nodes are the former.
To progress in the 3-phase commit requires responses from 2F+1 nodes; so you need ~ 2/3 of the nodes to respond appropriately to reach consensus (7 out of 10 in the case F=3).