In 1951, Kenneth Arrow proved that it is not possible to have a group decision making procedure that satisfies reasonable requirements like fairness. From the theoretical viewpoint, this is a great result -- well-deserving the Nobel Prize that was awarded to Professor Arrow. However, from the practical viewpoint, the question remains -- so how should we make group decisions? A usual way to solve this problem is to provide some reasonable heuristic ideas, but the problem is that different seemingly reasonable idea often lead to different group decision -- this is known, e.g., for different voting schemes. In this paper, we analyze this problem from the viewpoint of decision theory, the basic theory underlying all our activities -- including economic ones -- and describe the corresponding recommendations. Most of the resulting recommendations have been proposed earlier. The main objective of this paper is to provide a unified coherent narrative that leads from the fundamental first principles to practical recommendations.