Social welfare functions when preferences are convex,strictly monotonic,and continuous

The paper shows that if the class of admissible preference orderings is restricted in a manner appropriate for economic and political models, then Arrow's impossibility theorem for social welfare functions continues to be valid. Specifically if the space of alternatives is R ₊ ⁿ , n ≥ 3, where each dimension represents a different public good and if each person's preferences are restricted to be convex, continuous, and strictly monotonic, then no social welfare function exists that satisfies unanimity, independence of irrelevant alternatives, and nondictatorship.