Second-order induction in prediction problems

Rossella Argenziano, Itzhak Gilboa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)10323-10328
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number21
StatePublished - 2019


  • Belief formation
  • Empirically optimal similarity function
  • Generalized context model
  • Kernel estimation
  • Learning


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