IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v152y2014icp356-381.html
   My bibliography  Save this article

Optimal categorization

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053114000477
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2014.03.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. I. Gilboa & W. A. Postlewaite & D. Schmeidler, 2009. "Probability and Uncertainty in Economic Modeling," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 10.
    3. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    4. 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.
    5. , & ,, 2007. "Valuation equilibrium," Theoretical Economics, Econometric Society, vol. 2(2), June.
    6. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    7. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
    8. 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.
    9. James Dow, 1991. "Search Decisions with Limited Memory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 1-14.
    10. , & ,, 2008. "Contagion through learning," Theoretical Economics, Econometric Society, vol. 3(4), December.
    11. 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..
    12. 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.
    13. 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.
    14. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Jehiel, Philippe & Mohlin, Erik, 2021. "Cycling and Categorical Learning in Decentralized Adverse Selection Economies," Working Papers 2021:11, Lund University, Department of Economics.
    3. 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.
    4. Yasar, Alperen, 2023. "Power struggles and gender discrimination in the workplace," SocArXiv t4g83, Center for Open Science.
    5. Mengel, Friederike & Sciubba, Emanuela, 2014. "Extrapolation and structural similarity in games," Economics Letters, Elsevier, vol. 125(3), pages 381-385.
    6. Chollete, Loran & Schmeidler, David, 2014. "Demand-Theoretic Approach to Choice of Priors," UiS Working Papers in Economics and Finance 2014/14, University of Stavanger.
    7. Bleile, Jörg, 2016. "Categorization based Belief formations," Center for Mathematical Economics Working Papers 519, Center for Mathematical Economics, Bielefeld University.
    8. Philippe Jehiel & Erik Mohlin, 2023. "Categorization in Games: A Bias-Variance Perspective," Working Papers halshs-04154272, HAL.
    9. Simon Gleyze & Philippe Jehiel, 2023. "Expectation Formation, Local Sampling and Belief Traps: A new Perspective on Education Choices," Working Papers halshs-04154324, HAL.
    10. 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.
    11. 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.
    12. Daskalova, Vessela & Vriend, Nicolaas J., 2021. "Learning frames," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 78-96.
    13. Halpern, Joe & Heller, Yuval & Winter, Eyal, 2022. "The Benefits of Coarse Preferences," MPRA Paper 111670, University Library of Munich, Germany.
    14. Ellingsen, Tore & Mohlin, Erik, 2019. "Decency," Working Papers 2019:3, Lund University, Department of Economics.
    15. 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".
    16. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).
    17. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).
    18. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    2. Jehiel, Philippe & Singh, Juni, 2021. "Multi-state choices with aggregate feedback on unfamiliar alternatives," Games and Economic Behavior, Elsevier, vol. 130(C), pages 1-24.
    3. Daskalova, Vessela & Vriend, Nicolaas J., 2021. "Learning frames," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 78-96.
    4. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).
    5. Philippe Jehiel & Erik Mohlin, 2023. "Categorization in Games: A Bias-Variance Perspective," Working Papers halshs-04154272, HAL.
    6. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).
    7. Lensberg, Terje & Schenk-Hoppé, Klaus Reiner, 2021. "Cold play: Learning across bimatrix games," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 419-441.
    8. Yasar, Alperen, 2023. "Power struggles and gender discrimination in the workplace," SocArXiv t4g83, Center for Open Science.
    9. Azrieli, Yaron, 2010. "Categorization and correlation in a random-matching game," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 303-310, May.
    10. Christoph March, 2011. "Adaptive social learning," Working Papers halshs-00572528, HAL.
    11. Grimm, Veronika & Mengel, Friederike, 2012. "An experiment on learning in a multiple games environment," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2220-2259.
    12. Philippe Jehiel & Jakub Steiner, 2020. "Selective Sampling with Information-Storage Constraints [On interim rationality, belief formation and learning in decision problems with bounded memory]," The Economic Journal, Royal Economic Society, vol. 130(630), pages 1753-1781.
    13. Marco LiCalzi & Roland Mühlenbernd, 2022. "Feature-weighted categorized play across symmetric games," Experimental Economics, Springer;Economic Science Association, vol. 25(3), pages 1052-1078, June.
    14. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    15. Rossella Argenziano & Itzhak Gilboa, 2012. "History as a coordination device," Theory and Decision, Springer, vol. 73(4), pages 501-512, October.
    16. Sendhil Mullainathan & Joshua Schwartzstein & Andrei Shleifer, 2008. "Coarse Thinking and Persuasion," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(2), pages 577-619.
    17. Joseph Y. Halpern & Yuval Heller & Eyal Winter, 2022. "The Benefits of Coarse Preferences," Papers 2201.10141, arXiv.org, revised Jun 2023.
    18. Olivier Gossner & Jakub Steiner, 2016. "Optimal Illusion of Control and Related Perception Biases," Edinburgh School of Economics Discussion Paper Series 276, Edinburgh School of Economics, University of Edinburgh.
    19. Steiner, Jakub & Stewart, Colin, 2015. "Price distortions under coarse reasoning with frequent trade," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 574-595.
    20. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Misinterpreting Others and the Fragility of Social Learning," Econometrica, Econometric Society, vol. 88(6), pages 2281-2328, November.

    More about this item

    Keywords

    Categorization; Priors; Coarse reasoning; Similarity-based reasoning; Case-based reasoning; Regression trees;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:152:y:2014:i:c:p:356-381. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.