Duality in the Theory of Social Choice

Abstract

Duality has been explored in many branches of Economic Theory, as for instance the duality between cost and production or between expenditure and utility. A start has been made in [5] to investigate duality between demand correspondences and budget correspondences in the theory of social choice. We shall study a society which acts according to a social preference relation given on a family of budget sets b. For all alternatives x of X, a set of alternatives, the budget correspondence will assign all those budgets to x, which are the minimal elements of the family of budget sets, in which x is available. On the other side, a choice correspondence assigns the maximal elements x of B to every budget $B \subseteq X$, given a social preference relation on X. Therefore, the budget correspondences are considered as the dual counterparts to choice correspondences.