Second-Order Induction and Agreement

Agents make predictions based on similar past cases. The notion of similarity is itself learnt from experience by "second-order induction": past cases inform agents also about the relative importance of various attributes in judging similarity. However, there may be multiple "optimal" similarity functions for explaining past data. Moreover, the computation of the optimal similarity function is NP-Hard. We offer conditions under which rational agents who have access to the same observations are likely to converge on the same predictions, and conditions under which they may entertain different probabilistic beliefs.