I think your statics are flawed. To give equal weight to each person's opinion we should assume that each person has an independent probability, p, of being right. Then the probability of Zed being right and the others being wrong would be p (1-p)^10 while the probability of the others being right and Zack being would be p^10 (1-p). Since these events are disjoint the probability Zack being right given that one of these two events occured would p (1-p)^10 / (p (1-p)^10 + p^10 (1-p)) = (1-p)^9 / ((1-p)^9 + p^9) while the probability of the others being right would be p^9 / ((1-p)^9 + p^9). Thus if p is less than 1/2 then Zed is more likely to be correct.