Something I've wondered about Paxos: does the voting not rely on knowing how many voters there are, to see if there is a majority?
That makes it harder to survive a network partition, right?
As to your question, it really depends what you mean by "survive". Paxos will not make progress unless it can achieve quorum, usually set as the majority of nodes. However it won't corrupt data either (multiple different tx values being chosen during consensus). It is thus a good fit for non-adversarial environments where you own & control all the nodes in the cluster and want to gracefully handle common faults (nodes losing power or crashing, network messages lost).
The larger pool can still have majority, but the smaller pool can not. Does the smaller pool change membership (because it can't see the larger pool) and continues on it's own? What if the smaller pool has a cold start and has no idea about the larger pool?
My point is that there needs to be some consensus on pool size to decide what constitutes a majority vote.
Implementations can make reasonable assumptions and rules for this, but afaict it's not covered by the protocol itself.