Simplicity and likelihood: An axiomatic approach

Itzhak Gilboa*, David Schmeidler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We suggest a model in which theories are ranked given various databases. Certain axioms on such rankings imply a numerical representation that is the sum of the log-likelihood of the theory and a fixed number for each theory, which may be interpreted as a measure of its complexity. This additive combination of log-likelihood and a measure of complexity generalizes both the Akaike Information Criterion and the Minimum Description Length criterion, which are well known in statistics and in machine learning, respectively. The axiomatic approach is suggested as a way to analyze such theory-selection criteria and judge their reasonability based on finite databases.

Original languageEnglish
Pages (from-to)1757-1775
Number of pages19
JournalJournal of Economic Theory
Issue number5
StatePublished - Sep 2010


  • Akaike Information Criterion
  • Axioms
  • Maximum likelihood
  • Minimum Description Length
  • Model selection
  • Simplicity


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