  We consider social welfare functions that satisfy Arrow's classic axioms of
independence of irrelevant alternatives and Pareto optimality when the outcome
space is the convex hull of some finite set of alternatives. Individual and
collective preferences are assumed to be continuous and convex, which
guarantees the existence of maximal elements and the consistency of choice
functions that return these elements, even without insisting on transitivity.
We provide characterizations of both the domains of preferences and the social
welfare functions that allow for anonymous Arrovian aggregation. The domains
admit arbitrary preferences over alternatives, which completely determine an
agent's preferences over all mixed outcomes. On these domains, Arrow's
impossibility turns into a complete characterization of a unique social welfare
function, which can be readily applied in settings involving divisible
resources such as probability, time, or money.
