Consistent updating of social welfare functions

Abstract

It is one of the central doctrines for ‘rational’ decision making that an agent should be forward-looking and not be bound by bygones. We argue that this is not an appealing principle for collective decision making, and that bygones have necessary and substantive roles. We consider an explicitly dynamic process of social welfare orderings, and propose a dynamic constraint which is acceptable even after rejecting the principle that one should be forward-looking. It is a conjunction of two assertions: (i) the process must be dynamically consistent, which means an ex ante welfare judgment must be respected by the ex post ones and there should be no contradiction between them; (ii) the structure of a welfare judgment should be recurrent under consistent updating, in the sense that if a postulate is satisfied by an ex ante welfare judgment, then it is also satisfied by any of the ex post ones that follow this ex ante judgment. Based on this standpoint, we present a set of axioms for social welfare orderings which are recurrent under consistent updating, and characterize a set of social welfare functions which are closed under updating. With such a class of social welfare functions, we characterize the roles that can be played in the updating stage by the past and things known not to have occurred.