My answer: any form of arbitrary authority is authoritarianism. Authority not based on both harm avoidance and reciprocity is arbitrary. Authority, at least in a free society, cannot be its own moral root. Purity also has to be further supported by both harm avoidance and reciprocity or it is Puritanism. In-group loyalty in a free society, must be supported by both harm avoidance and reciprocity or it is fascism.