Consistent updating of social welfare functions

It is one of the central doctrines for ”rational” decision making that an agent should be forward-looking and not be bound by things already gone. We argue that this is not an appealing principle for collective decision making, and that things already gone have necessary and substantive roles. We consider a dynamic process of social welfare orderings explicitly, and propose a discipline which is acceptable even after rejecting the forward-lookingness principle. 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 ex-post ones and there should be no contradiction between them; (ii) a meaningful normative postulate should be recurrent under consistent updating, in the sense that a postulate met by an ex-ante welfare judgment is met by any of ex-post ones as its own property. 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 class of social welfare functions, we characterize the roles for pasts and things known not to occur, which are played in the updating stage. ∗I thank Chris Chambers for helpful comments and discussions, seminar participants at Michigan, QMUL, Kyoto, Kobe, Hitotsubashi, Osaka, Yeshiva, Exeter, St. Andrews and conference participants at RUD 2011 for helpful comments. †Department of Economics, University of Texas at Austin, BRB 1.116, Austin, TX 78712. Email: [email protected].