@Jack-Waugh you’re right about For-and-Against, the modification I suggested is much less significant because it requires the pairs to match exactly, whereas For-and-Against counts all the positives and all the negatives. Just another example of how arbitrary the concept of “balance” in this formalism is. I liked your strengthening of the argument, you’re absolutely right about that as well, because it virtually eliminates any level of information voters might have about other ballots.
Maybe there is something more tangible that F-balance is trying to point to, but it isn’t clear what it might be. In my opinion, with respect to the concept of balance, the strengthened construction should by all reason send equal.vote back to the drawing board, especially if they can’t even formalize a valid counter-argument.