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Optimal categorization

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  • Mohlin, Erik

Abstract

This paper studies categorizations that are optimal for the purpose of making predictions. A subject encounters an object (x,y). She observes the first component, x, and has to predict the second component, y. The space of objects is partitioned into categories. The subject determines what category the new object belongs to on the basis of x, and predicts that its y-value will be equal to the average y-value among the past observations in that category. The optimal categorization minimizes the expected prediction error. The main results are driven by a bias-variance trade-off: The optimal size of a category around x, is increasing in the variance of y conditional on x, decreasing in the variance of the conditional mean, decreasing in the size of the data base, and decreasing in the marginal density over x.

Suggested Citation

  • Mohlin, Erik, 2014. "Optimal categorization," Journal of Economic Theory, Elsevier, vol. 152(C), pages 356-381.
    • Handle: RePEc:eee:jetheo:v:152:y:2014:i:c:p:356-381
    DOI: 10.1016/j.jet.2014.03.007
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    1. Itzhak Gilboa & Andrew W. Postlewaite & David Schmeidler, 2008. "Probability and Uncertainty in Economic Modeling," Journal of Economic Perspectives, American Economic Association, vol. 22(3), pages 173-188, Summer.
    2. Fryer Roland & Jackson Matthew O., 2008. "A Categorical Model of Cognition and Biased Decision Making," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-44, February.
    3. , & ,, 2007. "Valuation equilibrium," Theoretical Economics, Econometric Society, vol. 2(2), June.
    4. , & ,, 2008. "Contagion through learning," Theoretical Economics, Econometric Society, vol. 3(4), December.
    5. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
    6. Punj, Girish & Moon, Junyean, 2002. "Positioning options for achieving brand association: a psychological categorization framework," Journal of Business Research, Elsevier, vol. 55(4), pages 275-283, April.
    7. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    8. James Dow, 1991. "Search Decisions with Limited Memory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 1-14.
    9. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2007. "Probabilities in Economic Modeling," PIER Working Paper Archive 07-023, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    10. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2012. "Empirical Similarity," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 9, pages 211-243, World Scientific Publishing Co. Pte. Ltd..
    11. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    12. Jehiel, Philippe & Koessler, Frédéric, 2008. "Revisiting games of incomplete information with analogy-based expectations," Games and Economic Behavior, Elsevier, vol. 62(2), pages 533-557, March.
    13. Joshua Coval & Jakub Jurek & Erik Stafford, 2009. "The Economics of Structured Finance," Journal of Economic Perspectives, American Economic Association, vol. 23(1), pages 3-25, Winter.
    14. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    15. Azrieli, Yaron, 2009. "Categorizing others in a large game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 351-362, November.
    16. Basu, Kaushik, 1994. "The Traveler's Dilemma: Paradoxes of Rationality in Game Theory," American Economic Review, American Economic Association, vol. 84(2), pages 391-395, May.
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    Cited by:

    1. Natalia Shestakova, 2010. "Pricing Scheme Choice: How Process Affects Outcome," CERGE-EI Working Papers wp411, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    2. Nicolò Barbieri & Kerstin Hotte & Peter Persoon, 2025. "The evolving boundary of green technology," SEEDS Working Papers 0325, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised Mar 2025.
    3. Jehiel, Philippe & Mohlin, Erik, 2021. "Cycling and Categorical Learning in Decentralized Adverse Selection Economies," Working Papers 2021:11, Lund University, Department of Economics.
    4. Yuval Heller & Eyal Winter, 2016. "Rule Rationality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 997-1026, August.
    5. Nicol`o Barbieri & Kerstin Hotte & Peter Persoon, 2025. "The evolving boundary of green technology," Papers 2503.21310, arXiv.org.
    6. Yasar, Alperen, 2023. "Power struggles and gender discrimination in the workplace," SocArXiv t4g83, Center for Open Science.
    7. Ran Spiegler, 2025. "Machine-Learning to Trust," Papers 2507.10363, arXiv.org, revised Nov 2025.
    8. Mengel, Friederike & Sciubba, Emanuela, 2014. "Extrapolation and structural similarity in games," Economics Letters, Elsevier, vol. 125(3), pages 381-385.
    9. Chollete, Loran & Schmeidler, David, 2014. "Demand-Theoretic Approach to Choice of Priors," UiS Working Papers in Economics and Finance 2014/14, University of Stavanger.
    10. Bleile, Jörg, 2016. "Categorization based Belief formations," Center for Mathematical Economics Working Papers 519, Center for Mathematical Economics, Bielefeld University.
    11. Philippe Jehiel & Erik Mohlin, 2023. "Categorization in Games: A Bias-Variance Perspective," Working Papers halshs-04154272, HAL.
    12. Simon Gleyze & Philippe Jehiel, 2023. "Expectation Formation, Local Sampling and Belief Traps: A new Perspective on Education Choices," Working Papers halshs-04154324, HAL.
    13. Mohlin, Erik & Östling, Robert & Wang, Joseph Tao-yi, 2020. "Learning by similarity-weighted imitation in winner-takes-all games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 225-245.
    14. Topi Miettinen, 2012. "Paying attention to payoffs in analogy-based learning," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 193-222, May.
    15. Daskalova, Vessela & Vriend, Nicolaas J., 2021. "Learning frames," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 78-96.
    16. Halpern, Joseph Y. & Heller, Yuval & Winter, Eyal, 2025. "The benefits of coarse preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 229(C).
    17. Halpern, Joe & Heller, Yuval & Winter, Eyal, 2022. "The Benefits of Coarse Preferences," MPRA Paper 111670, University Library of Munich, Germany.
    18. Ellingsen, Tore & Mohlin, Erik, 2019. "Decency," Working Papers 2019:3, Lund University, Department of Economics.
    19. Ennio Bilancini & Leonardo Boncinelli, 2014. "Persuasion with Reference Cues and Elaboration Costs," Center for Economic Research (RECent) 102, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    20. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).
    21. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).
    22. Bilancini, Ennio & Boncinelli, Leonardo, 2018. "Rational attitude change by reference cues when information elaboration requires effort," Journal of Economic Psychology, Elsevier, vol. 65(C), pages 90-107.

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    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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