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Random Categorization and Bounded Rationality

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Abstract
In this study we introduce a new stochastic choice rule that categorizes objects in order to simplify the choice procedure. At any given trial, the decision maker deliberately randomizes over mental categories and chooses the best item according to her utility function within the realized consideration set formed by the intersection of the mental category and the menu of alternatives. If no alternative is present both within the considered mental category and within the menu the decision maker picks the default option. We provide the necessary and sufficient conditions that characterize this model in a complete stochastic choice dataset in the form of an acyclicicity restriction on a stochastic choice revealed preference and other regularity conditions. We recover the utility function uniquely up to a monotone transformation and the probability distribution over mental categories uniquely. This model is able to accommodate violations of IIA (independence of irrelevant alternatives), of stochastic transitivity, and of the Manzini-Mariotti menu independence notion (i-Independence). A generalization of the categorizing procedure accommodates violations of regularity and thus provides an alternative model to random utility.

Suggested Citation

  • Victor H. Aguiar, 2016. "Random Categorization and Bounded Rationality," University of Western Ontario, Departmental Research Report Series 20163, University of Western Ontario, Department of Economics.
    • Handle: RePEc:uwo:uwowop:20163
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    File URL: https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1809&context=economicsresrpt
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    References listed on IDEAS

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    1. Paola Manzini & Marco Mariotti, 2012. "Categorize Then Choose: Boundedly Rational Choice And Welfare," Journal of the European Economic Association, European Economic Association, vol. 10(5), pages 1141-1165, October.
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    9. Echenique, Federico & Saito, Kota & Tserenjigmid, Gerelt, 2018. "The perception-adjusted Luce model," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 67-76.
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    Cited by:

    1. Demirkan, Yusufcan & Kimya, Mert, 2020. "Hazard rate, stochastic choice and consideration sets," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 142-150.
    2. Furtado, Bruno A. & Nascimento, Leandro & Riella, Gil, 2023. "Rational choice with full-comparability domains," Journal of Economic Behavior & Organization, Elsevier, vol. 216(C), pages 124-135.
    3. Ahumada, Alonso & Ülkü, Levent, 2018. "Luce rule with limited consideration," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 52-56.
    4. Victor H. Aguiar & Maria Jose Boccardi & Nail Kashaev & Jeongbin Kim, 2023. "Random utility and limited consideration," Quantitative Economics, Econometric Society, vol. 14(1), pages 71-116, January.
    5. Aguiar, Victor H. & Kimya, Mert, 2019. "Adaptive stochastic search," Journal of Mathematical Economics, Elsevier, vol. 81(C), pages 74-83.
    6. Horan, Sean, 2019. "Random consideration and choice: A case study of “default” options," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 73-84.
    7. Kovach, Matthew & Ülkü, Levent, 2020. "Satisficing with a variable threshold," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 67-76.
    8. Victor H. Aguiar & Nail Kashaev, 2019. "Identification and Estimation of Discrete Choice Models with Unobserved Choice Sets," Papers 1907.04853, arXiv.org, revised Jun 2021.
    9. Kovach, Matthew & Suleymanov, Elchin, 2023. "Reference dependence and random attention," Journal of Economic Behavior & Organization, Elsevier, vol. 215(C), pages 421-441.
    10. Roy Allen & John Rehbeck, 2020. "Identification of Random Coefficient Latent Utility Models," Papers 2003.00276, arXiv.org.
    11. Nail Kashaev & Natalia Lazzati, 2019. "Peer Effects in Random Consideration Sets," Papers 1904.06742, arXiv.org, revised May 2021.
    12. Matthew Ryan, 2019. "Generalised Random Categorisation Rules," Working Papers 2019-03, Auckland University of Technology, Department of Economics.
    13. Chambers, Christopher P. & Liu, Ce & Rehbeck, John, 2020. "Costly information acquisition," Journal of Economic Theory, Elsevier, vol. 186(C).
    14. Kashaev, Nail & Aguiar, Victor H., 2022. "A random attention and utility model," Journal of Economic Theory, Elsevier, vol. 204(C).
    15. Gibbard, Peter, 2021. "Disentangling preferences and limited attention: Random-utility models with consideration sets," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    16. Bhattacharya, Mihir & Mukherjee, Saptarshi & Sonal, Ruhi, 2021. "Frame-based stochastic choice rule," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    17. Yaron Azrieli & John Rehbeck, 2022. "Marginal stochastic choice," Papers 2208.08492, arXiv.org.
    18. Efe A. Ok & Gerelt Tserenjigmid, 2023. "Measuring Stochastic Rationality," Papers 2303.08202, arXiv.org, revised Dec 2023.
    19. Dazhuo Wei, 2024. "Random Attention Span," Papers 2405.11578, arXiv.org.
    20. Roy Allen, 2024. "Exogenous Consideration and Extended Random Utility," Papers 2405.13945, arXiv.org.
    21. Rehbeck, John, 2024. "A menu dependent Luce model with a numeraire," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    22. Yegane, Ece, 2022. "Stochastic choice with limited memory," Journal of Economic Theory, Elsevier, vol. 205(C).
    23. Manzini, Paola & Mariotti, Marco & Ülkü, Levent, 2024. "A model of approval with an application to list design," Journal of Economic Theory, Elsevier, vol. 217(C).
    24. Edward Honda, 2021. "Categorical consideration and perception complementarity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 693-716, March.
    25. Gerelt Tserenjigmid, 2021. "The Order-Dependent Luce Model," Management Science, INFORMS, vol. 67(11), pages 6915-6933, November.

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    More about this item

    Keywords

    Decision Theory; Random Choice; Bounded Rationality; Categorization; Consideration Sets;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D10 - Microeconomics - - Household Behavior - - - General

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