DYNAMICS OF INDUCTIVE INFERENCE IN A UNIFIED FRAMEWORK By

We present a model of inductive inference that includes, as special cases, Bayesian reasoning, case-based reasoning, and rulebased reasoning. This unified framework allows us to examine, positively or normatively, how the various modes of inductive inference can be combined and how their relative weights change endogenously. We establish conditions under which an agent who does not know the structure of the data generating process will decrease, over the course of her reasoning, the weight of credence put on Bayesian vs. non-Bayesian reasoning. We show that even random data can make certain theories seem plausible and hence increase the weight of rule-based vs. case-based reasoning, leading the agent in some cases to cycle between being rule-based and case-based. We identify conditions under which minmax regret criteria will not be effective. We thank Dirk Bergemann, Eddie Dekel, Drew Fudernberg, Gabi Gayer, Offer Lieberman, George Mailath, the editors and three referees for comments and suggestions. Tel-Aviv University, HEC, Paris, and Cowles Foundation, Yale University. ISF Grant 396/10 and ERC Grant 269754 are gratefully acknowledged. Department of Economics, Yale University. National Science Foundation grant SES0850263 is gratefully acknowledged. The Ohio State University and Tel-Aviv University. Dynamics of Inductive Inference in a Unified Framework Itzhak Gilboa, Larry Samuelson, David Schmeidler February 4, 2011