Impossibility Theorems for Menu Dependent Preference Functionals

We consider functions that assign to each evaluation profile a preference system or a list of menu dependent preferences. The rule by which such an assignment takes place is said to be a menu dependent preference functional (MDPFL). We extend the concepts of invariance under individual cardinal transformations, weak Pareto, binary independence, weak dictatorship and veto power from the context of social welfare functionals to our framework of MDPFL's. We consider admissible sets of evaluation profiles which are slightly more general than necessarily requiring that all evaluation profiles be admissible. We introduce the concepts of nested and nested* MDPFL's. Our first result says that a nested MDPFL which is invariant under individual transformations, globally weakly Paretian and satisfies global binary independence must be weakly dictatorial. Our second result says that a nested* MDPFL which is invariant under individual transformations, globally weakly Paretian and satisfies global binary independence must have an individual/criterion that wields veto power. And satisfies binary independence must have an individual/criterion that wields veto power