If every participant is online and all messages are public, then only a majority vote is necessary, as time itself becomes exclusive (only earlier votes matter)

If every participant is online and all messages are public, then only a majority vote is necessary, as time itself becomes exclusive (only earlier votes matter). There's no need for PoW here. For participants that join later both PoW and PoS are probabilistic, but PoS can be much better: if everyone has to vote the maximum possible classical security is 1-of-n, ie. one eternally honest party exists in all past blocks, so no attacker can obtain 100%, ever. This model can stall but it can't lie. The 100% model is not practical and by itself requires everyone to be online, but for some m in m-of-n, it is. Another variable is how long do the honest assumption must hold: it's relatively easy to construct a scheme that makes honesty for eg. four months nearly certain. Combined with the fact that money is inherently a social thing, it works. It's not an abstract consensus for people in bunkers, but people that want to interact. So if you return after a long time, it's enough to check in several places that accept a specific cryptocurrency what chain is wanted by them.