The network is autonomous, it follows rules. A transfer of digital info is atomic and uses a cryptographic signature to show the last person who owned it has singed the coin over to the current owner. When the current owner spends, then he asks the network to accept a signed message transferring ownership to the new owner. Imagine a coin looks like this
----------------------
CurrentOwnerID
----------------------
Previous owner ID
----------------------
Signature of previous owner
(signs whole coin)
This coin is kept in several groups who are all calculable (groups close to coin name, hash of coin name and hash of that again). Each group mus syncronise the ownership xfer (only one winner) and then the groups sync themselves (again only one winner).
Anyone reading the coin from the network get the current owner as all groups return what they believe is current owner (majority rules when syncronising, otherwise they all match). Any non collaborating group is reported and deranked. effectively moving bad nodes away. To attack a single group requires circa 3 times the current network size of nodes of rank capable of forming a group. Network picks ID for you so no targetting of where you get on the network. So attack becomes much higher than 80% and the more attackers the more safe it is (as each attacker prevents others getting majorities), more users achieve the same thing.
tl:dr
Its all a kinda magic 