> the longest chain rule (LCR) [1]. In your system, what's the rule?
There is no direct equivalent to the longest chain rule because blocks are final on every chain. There is no "chain switching" possible (that would directly contradict finality). Instead the system is made so that forks dont happen. The system will produce empty blocks rather than fork if the 80% quorum can not be reached (for example if huge parts of the world are temporary discontented from each-other).
So any actual fork would need to be intentional and thus actually produce 2 immutable chains in 2 different networks with finality. Nodes wont be able to switch between these chains, the intentional fork separates the network. If a nodes wants to switch later on that is the equivalent of turning it off and starting a new one on the other chain.
BTW this is not MY system its been implemented multiple times with the oldest running since 9+ years [1]. It has never forked so this is not an actual problem in the real world. Dude to the quorum of 80% every change (in the code) goes trough an amendment process and will only ever get activated if it has 80% support. If a node is overruled it still is on the same chain. Unless the owner refuses to update in time then his node becomes incompatible with the rest and is ignored.
[1]The oldest running distributed ledger ("blockchain") that uses this system is the XRPL. You can read about its consensus mechanism on xrpl.org/intro-to-consensus.html and xrpl.org/consensus-network.html There are ofc many other projects that build upon the same principles.
So, when a new node comes online, and some of the existing nodes say that they've agreed on B1 and B2, and some other nodes say that they've agreed on B1' and B2', how does that new node decide which is the consensus? [0] With PoW, the decision criterion is easy: the longest chain rule (LCR) [1]. In your system, what's the rule?
[0] This is trivial with a central authority. But remember, here we have an open public blockchain, where anyone can join as a node, and they might be malicious.
[1] And as long as there are competing chains of equal length, just pick one randomly. That procedure, rather than picking the first one encountered, improves resistance to the selfish mining attack, IIRC