In 1951, K.J. Arrow proved that, under certain assumptions, it is impossible to have group decision-making rules that satisfy reasonable conditions like symmetry. This Impossibility Theorem is often cited as a proof that reasonable group decision-making is impossible. We start our article by remarking that Arrow's result covers only those situations when the only information we have about individual preferences is their binary preferences between the alternatives. If we follow the main ideas of modern decision making and game theory and also collect information about the preferences between lotteries (i.e., collect the utility values of different alternatives), then reasonable decision-making rules are possible, e.g., Nash's rule in which we select an alternative for which the product of utilities is the largest possible. We also deal with two related issues: how we can detect individual preferences if all we have is preferences of a subgroup and how we take into account the mutual attraction between participants.

When computing a square root, computers still, in effect, use an iterative algorithm developed by the Babylonians millennia ago. This is a very unusual phenomenon, because for most other computations, better algorithms have been invented - even division is performed, in the computer, by an algorithm which is much more efficient that division methods that we have all learned in school. What is the explanation for the success of the Babylonians' method? One explanation is that this is, in effect, Newton's method, based on the beast ideas from calculus. This explanations works well from the mathematical viewpoint - it explains why this method is so efficient, but since the Babylonians were very far from calculus, it does not explain why this method was invented in the first place. In this paper, we provide two possible explanations for this method's origin. We show that this method naturally emerges from fuzzy techniques, and we also show that it can be explained as (in some reasonable sense) the computationally simplest techniques.