IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2303.08202.html
   My bibliography  Save this paper

Measuring Stochastic Rationality

Author

Listed:
  • Efe A. Ok
  • Gerelt Tserenjigmid

Abstract

Our goal is to develop a partial ordering method for comparing stochastic choice functions on the basis of their individual rationality. To this end, we assign to any stochastic choice function a one-parameter class of deterministic choice correspondences, and then check for the rationality (in the sense of revealed preference) of these correspondences for each parameter value. The resulting ordering detects violations of (stochastic) transitivity as well as inconsistencies between choices from nested menus. We obtain a parameter-free characterization and apply it to some popular stochastic choice models. We also provide empirical applications in terms of two well-known choice experiments.

Suggested Citation

  • Efe A. Ok & Gerelt Tserenjigmid, 2023. "Measuring Stochastic Rationality," Papers 2303.08202, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2303.08202
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2303.08202
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ahumada, Alonso & Ülkü, Levent, 2018. "Luce rule with limited consideration," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 52-56.
    2. Jose Apesteguia & Miguel A Ballester, 2021. "Separating Predicted Randomness from Residual Behavior," Journal of the European Economic Association, European Economic Association, vol. 19(2), pages 1041-1076.
    3. Paola Manzini & Marco Mariotti, 2014. "Stochastic Choice and Consideration Sets," Econometrica, Econometric Society, vol. 82(3), pages 1153-1176, May.
    4. Ok, Efe A. & Tserenjigmid, Gerelt, 2022. "Indifference, indecisiveness, experimentation and stochastic choice," Theoretical Economics, Econometric Society, vol. 17(2), May.
    5. Georgios Gerasimou, 2018. "Indecisiveness, Undesirability and Overload Revealed Through Rational Choice Deferral," Economic Journal, Royal Economic Society, vol. 128(614), pages 2450-2479, September.
    6. Horan, Sean, 2021. "Stochastic semi-orders," Journal of Economic Theory, Elsevier, vol. 192(C).
    7. Jose Apesteguia & Miguel A. Ballester, 2015. "A Measure of Rationality and Welfare," Journal of Political Economy, University of Chicago Press, vol. 123(6), pages 1278-1310.
    8. Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, vol. 62(6), pages 1251-1289, November.
    9. Mark Dean & Daniel Martin, 2016. "Measuring Rationality with the Minimum Cost of Revealed Preference Violations," The Review of Economics and Statistics, MIT Press, vol. 98(3), pages 524-534, July.
    10. Drew Fudenberg & Ryota Iijima & Tomasz Strzalecki, 2015. "Stochastic Choice and Revealed Perturbed Utility," Econometrica, Econometric Society, vol. 83, pages 2371-2409, November.
    11. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    12. Faruk Gul & Paulo Natenzon & Wolfgang Pesendorfer, 2014. "Random Choice as Behavioral Optimization," Econometrica, Econometric Society, vol. 82, pages 1873-1912, September.
    13. Machina, Mark J, 1985. "Stochastic Choice Functions Generated from Deterministic Preferences over Lotteries," Economic Journal, Royal Economic Society, vol. 95(379), pages 575-594, September.
    14. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
    15. Jose Apesteguia & Miguel A. Ballester & Jay Lu, 2017. "Single‐Crossing Random Utility Models," Econometrica, Econometric Society, vol. 85, pages 661-674, March.
    16. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
    17. Aguiar, Victor H. & Serrano, Roberto, 2017. "Slutsky matrix norms: The size, classification, and comparative statics of bounded rationality," Journal of Economic Theory, Elsevier, vol. 172(C), pages 163-201.
    18. Aguiar, Victor H., 2017. "Random categorization and bounded rationality," Economics Letters, Elsevier, vol. 159(C), pages 46-52.
    19. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
    20. Fishburn, Peter C., 1992. "Induced binary probabilities and the linear ordering polytope: a status report," Mathematical Social Sciences, Elsevier, vol. 23(1), pages 67-80, February.
    21. Paulo Natenzon, 2019. "Random Choice and Learning," Journal of Political Economy, University of Chicago Press, vol. 127(1), pages 419-457.
    22. Echenique, Federico & Saito, Kota & Tserenjigmid, Gerelt, 2018. "The perception-adjusted Luce model," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 67-76.
    23. Eliaz, Kfir & Ok, Efe A., 2006. "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences," Games and Economic Behavior, Elsevier, vol. 56(1), pages 61-86, July.
    24. Manzini, Paola & Mariotti, Marco, 2018. "Dual random utility maximisation," Journal of Economic Theory, Elsevier, vol. 177(C), pages 162-182.
    Full references (including those not matched with items on IDEAS)

    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. Demirkan, Yusufcan & Kimya, Mert, 2020. "Hazard rate, stochastic choice and consideration sets," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 142-150.
    2. Duffy, Sean & Gussman, Steven & Smith, John, 2021. "Visual judgments of length in the economics laboratory: Are there brains in stochastic choice?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 93(C).
    3. 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.
    4. 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.
    5. Caliari, Daniele, 2023. "Rationality is not consistency," Discussion Papers, Research Unit: Economics of Change SP II 2023-304, WZB Berlin Social Science Center.
    6. Caliari, Daniele, 2023. "Behavioural welfare analysis and revealed preference: Theory and experimental evidence," Discussion Papers, Research Unit: Economics of Change SP II 2023-303, WZB Berlin Social Science Center.
    7. Gerelt Tserenjigmid, 2021. "The Order-Dependent Luce Model," Management Science, INFORMS, vol. 67(11), pages 6915-6933, November.
    8. Duffy, Sean & Smith, John, 2020. "An economist and a psychologist form a line: What can imperfect perception of length tell us about stochastic choice?," MPRA Paper 99417, University Library of Munich, Germany.
    9. Kashaev, Nail & Aguiar, Victor H., 2022. "A random attention and utility model," Journal of Economic Theory, Elsevier, vol. 204(C).
    10. Javier A. Birchenall, 2024. "Random choice and market demand," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 57(1), pages 165-198, February.
    11. Roy Allen & John Rehbeck, 2023. "Revealed stochastic choice with attributes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 91-112, January.
    12. Heydari, Pedram, 2021. "Luce arbitrates: Stochastic resolution of inner conflicts," Games and Economic Behavior, Elsevier, vol. 126(C), pages 33-74.
    13. Bhattacharya, Mihir & Mukherjee, Saptarshi & Sonal, Ruhi, 2021. "Frame-based stochastic choice rule," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    14. Yoram Halevy & David Walker-Jones & Lanny Zrill, 2023. "Difficult Decisions," Working Papers tecipa-753, University of Toronto, Department of Economics.
    15. Roy Allen & Pawel Dziewulski & John Rehbeck, 2019. "Revealed statistical consumer theory," Working Paper Series 1119, Department of Economics, University of Sussex Business School.
    16. Duffy, Sean & Gussman, Steven & Smith, John, 2019. "Judgments of length in the economics laboratory: Are there brains in choice?," MPRA Paper 93126, University Library of Munich, Germany.
    17. Federico Echenique & Kota Saito, 2019. "General Luce model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 811-826, November.
    18. Breitmoser, Yves, 2017. "Discrete Choice with Presentation Effects," Rationality and Competition Discussion Paper Series 35, CRC TRR 190 Rationality and Competition.
    19. Dongwoo Lee & Hans Haller, 2022. "Selective attribute rules," Journal of Economics, Springer, vol. 137(3), pages 229-254, December.
    20. Roy Allen & Paweł Dziewulski & John Rehbeck, 2024. "Revealed statistical consumer theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(3), pages 823-847, May.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2303.08202. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.