It is well known that the basic theorem of welfare economics (Every competitive equilibrium is a Pareto-optimum; and every Pareto-optimum is a competitive equilibrium) has been refuted by counterexamples on the production side (eg. external effects and increasing returns to scale), or as it is usually put, suffers from "exceptions". The purpose of this paper is to prove that there are counter examples, or "exceptions", on the preferences side as well, which impose further restrictions on the domain of validity of the theorem. In a society committed to the value judgement that social choices ought to be determined by the preferences of individual citizens, there arc two, alternative, methods of arriving at such choices, the market method, and the political method. In a famous book, 1 Arrow showed that the political method suffers from a grave weakness. This paper aims to demonstrate that the alternative method, the market method, also suffers from a grave weakness.