Random aggregation without the Pareto principle

Barberà-Sonnenschein (J Econ Theory 18:244–254, 1978) have shown that any binary and Paretian random social choice function can be associated with a mapping which associates a real number with each coalition of individuals. This function gives, for each coalition, the power that this group has in imposing on society, their common preference relation on a pair of alternatives. The aim of this paper is to extend this result, showing that the Pareto criterion is not a necessary condition for the existence of such a coalitional power function.