1. Impossibility Theorems for Menu-Dependent Preference Functional
2. Main Lemma Implies the Main Theorem
3. As F is nested, F A (U)?F X (U) and so (y,x)?F X (U), leading to a contradiction. Thus, (x,y)?P(F A (U)) for all A??(X) satisfying x,y?A and so i is a weak dictator;Suppose A??(X), with x,y?A and toward a contradiction suppose (x,y)?P(F A (U))
4. Theorem 3: Let F be a MDPFL on an admissible set D where D is rich and O N -representable. Suppose F is cardinally noncomparable, globally weakly Paretian, globally binarily independent, and nested * . Then, there exists i?N who/that has veto power. Proof: By Theorem 1, there exists i?N, such that for all U?D and x;Suppose F is cardinally noncomparable, weakly Paretian, binarily independent, and nested. Then, F must be weakly dictatorial
5. As (x,y)?F X (U)?(A?A), it must be the case that (x,y)?F A (U). Thus, (x,y)?F A (U) for all A??(X) satisfying x,y?A and so i has veto power;Suppose A?Y(X), with x,y?A. As F is nested * , F X (U)?(A?A) ? F A (U)