Indeed it appears his system needs to be modeled as a complex state machine.
You can't just make a claim out-of-context that an "honest" majority of the trust reputation will decide the winner of a double-spend. You have to model the state machine holistically before you can make any claim.
Proof-of-work eliminates that requirement because each new iteration of a block solution is
independent (trials, often simplistically modeled as a Poisson distribution) from the prior one (except to some small extent in selfish mining which is also easily modeled with a few equations). See the selfish-mining paper for the state machine and then imagine how complex the model for his design will be.
This is
independence is what I mean when I say the entropy of PoW is open (unbounded), while it is closed for PoS.[1]
Imagine this highly technical discussion comparing PoW and PoS can't happen in the Bitcoin Technical & Discussion forum, because the overlord Gregory Maxwell moves it to the Altcoin Discussion thread.