Rational budgeters in the theory of social choice

The purpose of this paper is to explore duality in the theory of social choice. As application Arrow's Impossibility Theorem and another impossibility theorem using the notion of positive responsiveness are chosen. It will be seen that we can establish notions and theorems which are symmetric to the original ones. However, if we establish impossibility theorems when rational behaviour is described by budget correspondences and not by choice correspondences, we need not assume that every subset of X (a family of alternatives) with cardinality 2 is a budget set. Therefore the dual theorems also may hold for families of competitive budget sets. It will also be shown that although the underlying preferences on X need not be acyclic, local decisiveness on budget sets may lead to global decisiveness on these sets.