We are working out some more formal numbers. But it roughly works like this:
Say I had way more stake than anyone else. In PoS, that means as if today, I can start building the longest chain myself and ignore everyone else's blocks.
In our PoP, even with so much stake, I can still only slowly cause my nodes to be added to the network over a long time, so it may take months or years before I become a 51% majority of nodes in the network.
To stay in the pool, it's not sufficient to just own the coins. I must also prove to the network that I am running the nodes. So there is at least some financial overhead to maintain the attack this long as well.
Consider that during this time, new coinbase will be created for those in the pool, and they may distribute it to people who are not the attacker, which would prevent the attacker from completing the attack.
