In this paper, we try first to shift the problem onto the agents. We want actually to consider some methods for passing from coalitions to lotteries over coalitions. These methods are associated with a function that could correspond to a social utility function. It gives the level of satisfaction coming from the anticipated "consumption" of a subset of alternatives (goods, candidates,..) by a coalition. Second, we want to define the distributions of power regardless of those two-element feasible sets which characterize preferences in basic models on one side, and we try to exhibit a theoretical relation between the basic Barberà & Sonnenschein’s model and ours thanks to the Choice Axiom of Luce 1959 on the other side. Third, McLennan’s argument against the validity of subadditivity for all power functions, i.e. the number of alternatives, disappears since we can introduce nonadditive lotteries directly from a Generalized Choice Axiom that can be obtained with the introduction of Choquet capacities. These latter, which appeared in Choquet 1953, were introduced in economics by Gilboa 1987 and Schmeidler 1989. They allow to weaken the standard constraints on probabilities in putting a simple condition of monotrmjcity in place of additivity. Finally, we try to prove that it is possible to deduce a ^cial or a coalitional utility function directly fromlotteries over preferences in implying a Power Scheme (i.e. a distribution of power decision) from the basic Social Welfare Scheme, this last being probabilistic or nonadditive