One way to make group decisions is to select the best decision maker(s) in the group as the authority, and to follow his or her decisions. At first glance, it seems that if the selected authority is indeed the best decision maker, it is beneficial for everyone to obey his or her authority. However, history shows that in many cases, challenges to the authority (even to the authority of the best decision maker) were beneficial to the group. In this paper, we provide an algorithmic explanation for this phenomenon. The main idea behind this explanation is that most practical general problems are NP-hard and thus, no feasible algorithm can solve all instances of such a problem. Thus, even for the best decision maker, who uses the best of the currently available feasible algorithms, there inevitably are cases when the resulting decision is not the best, and can thus be improved.