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Second-order induction in prediction problems

Author

Listed:
  • Rossella Argenziano

    (Department of Economics, University of Essex, Colchester CO4 3SQ, United Kingdom)

  • Itzhak Gilboa

    (Economics and Decision Sciences Department, École des Hautes Études Commerciales de Paris, 78351 Jouy-en-Josas Cedex, France; Berglas School of Economics, Tel-Aviv University, Tel Aviv 6997801)

Abstract

Agents make predictions based on similar past cases, while also learning the relative importance of various attributes in judging similarity. We ask whether the resulting “empirically optimal similarity function” (EOSF) is unique and how easy it is to find it. We show that with many observations and few relevant variables, uniqueness holds. By contrast, when there are many variables relative to observations, nonuniqueness is the rule, and finding the EOSF is computationally hard. The results are interpreted as providing 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.

Suggested Citation

  • Rossella Argenziano & Itzhak Gilboa, 2019. "Second-order induction in prediction problems," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 116(21), pages 10323-10328, May.
    • Handle: RePEc:nas:journl:v:116:y:2019:p:10323-10328
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