When we did the initial napkin design, we wanted a protocol that would allow for anything less than 1/2 of the witness to be behaving badly. So, the obvious worst case here would be 1/2 bad witnesses voting on two sides of a fork. In such a case, both forks would have 1/4 good witnesses + 1/2 bad witnesses and a 3/4ths majority would be achieved on both sides of the fork.