(In any non-Proof-of-Work design, ) It is mathematically impossible for there to be external consensus trust of the honest chain if the dishonest chain is controlled by more than 51% of the peers. We've covered some of the scenarios upthread, and it always boils down to that the external viewers can not know who to trust except by trusting the majority of peers.

The only mathematical way around this is to centralize the network, by placing more trust in some peers than others over time.

Indeed long-term reputation is a mathematically viable alternative to Proof-of-Work. This is centralization. There are tradeoffs.

So this is not "7 billion individually watching the network", but rather a fewer # of peers with reputation being trusted. This is just the political power vacuum all over again with its contingent problems of vested interests Olsen power scramble:

https://bitcointalk.org/index.php?topic=226033 (No Money Exists Without the Majority)

Notwithstanding the above, any non-Proof-of-Work system can be attacked with much less than 51% of the peers, due to the fact that the input entropy is preimageable, as I explained upthread. Again the only way to work around this is to trust some established peers to guard against this.