Second-Order Induction: Uniqueness and Complexity

43 Pages Posted: 15 May 2018

See all articles by Rossella Argenziano

Rossella Argenziano

University of Essex - Department of Economics

Itzhak Gilboa

Tel Aviv University - Eitan Berglas School of Economics; HEC Paris - Economics & Decision Sciences

Date Written: February 1, 2018

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 "empirical similarity" 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, non-uniqueness is the rule, and finding the best similarity function 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.

Keywords: Empirical Similarity, Belief Formation

Suggested Citation

Argenziano, Rossella and Gilboa, Itzhak, Second-Order Induction: Uniqueness and Complexity (February 1, 2018). HEC Paris Research Paper No. ECO/SCD-2018-1265. Available at SSRN: https://ssrn.com/abstract=3178712 or http://dx.doi.org/10.2139/ssrn.3178712

Rossella Argenziano (Contact Author)

University of Essex - Department of Economics ( email )

Wivenhoe Park
Colchester CO4 3SQ
United Kingdom

Itzhak Gilboa

Tel Aviv University - Eitan Berglas School of Economics ( email )

P.O. Box 39040
Ramat Aviv, Tel Aviv, 69978
Israel
972-3-640-6423 (Phone)
972-3-640-9908 (Fax)

HEC Paris - Economics & Decision Sciences

Paris
France

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