So I'm pretty a similar problem could exist. If to accept a proposal we only need 3 nodes, not a majority, and we manipulate network latency in arbitrarily bad ways, a similar split brain could occur. Basically, you could commit the same transaction twice under different proposal numbers.

Consensus is not about transactions, it's about agreeing on a value (a single value, strictly speaking, unlike atomic broadcast, which is about agreeing on a sequence of values, although people often identify the two). But anyway, your argument is not in any way concrete - try to come up with a counterexample. Having thought about it more, I am confident that the author's system is correct (in the sense that it always preserves agreement).

Sadly, what's even worse, is as I was reading this, I wondered if it might be an attempt to undermine the Democratic Party. The barrier for determining the origin of their funding and the organizational composition of the group is also high enough that I don't know how to figure out trustworthiness...