More exactly, >= 2/3 must be honest (<1/3 may be malicious).
From ABA’s BV broadcast, no estimate coming from <1/3 of the nodes will propagate. From this behaviour follows that they won’t be able to dictate an incorrect value.
I think that the weird things about the diagram I mentioned above are simply due to the block being invalid. A valid block is a block voted for by a supermajority of nodes. Here N=4 and the vote is true for only 2 nodes, which is not enough to make it valid (because 2/3N = 2.66 > 2).
The requirements are not met to trigger a meta election. It is a pity is that this diagram is used in the parsec paper to illustrate meta-election (on page 6):
This is a very bad example because the block is not valid.
When the requirements are met (an event strongly sees a valid block), then current node knows that the block will be agreed on eventually. The meta election only determines the order of the block, so counter intuitive actions can be done like:
adding an estimate different from what a node voted for in the past
using randomness by flipping a coin
The aim is only to get a consensus on the order of the block. If it were to determine the block validity, then these actions would be effectively absurd.
I have to say, while it’s flattering, it’s tiring to be constantly reduced to one’s looks… Of course, as the third ever best looking employee, you wouldn’t be able to put yourself in my shoes; but you know… It feels a bit objectifying… Sometimes I just want to tell the world: I’m more than just a pretty face