Theories and cases in decisions under uncertainty

We present and axiomatize a model combining and generalizing theory-based and analogy-based reasoning in decision under uncertainty. An agent has beliefs over a set of theories describing the data generating process, given by decision weights. She also puts weight on similarity to past cases. When a case is added to her memory and a new problem is encountered, two types of learning take place. First, the decision weight assigned to each theory is multiplied by its conditional probability. Second, subsequent problems are assessed for their similarity to past cases, including the newly-added case. If no weight is put on past cases, the model is equivalent to Bayesian reasoning over the theories. However, when this weight is positive, the learning process continually adjusts the balance between case-based and theory-based reasoning. In particular, a “black swan” which is considered a surprise by all theories would shift the weight to case-based reasoning.