But let's say our "gender-bias free" method leads a manager to hire 7 men and 3 women. This leads the manager to draw the conclusion that "My next hire is more likely to be a male than a female". The manager wants to acquire a good candidate pool as quickly as possible, so now he changes his mental search heuristic to favor male applicants, if he can discern their gender.

Haven't we just reinforced his bias further, now cemented by hard fact (and faulty reasoning)?

edit: missed a word