IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2606.15740.html

Axioms and Anomalies with Finite Data

Author

Listed:
  • Cheaheon Lim
  • Tomasz Strzalecki

Abstract

The classical expected utility (EU) axioms are not sufficient for finite datasets. There are a number of anomalies (violations of EU) where axioms are satisfied. This paper studies axioms that are immune to this problem and definitively delineate between EU and non-EU. We discuss implications for experimental design and explore the automatic generation of anomalies.

Suggested Citation

  • Cheaheon Lim & Tomasz Strzalecki, 2026. "Axioms and Anomalies with Finite Data," Papers 2606.15740, arXiv.org, revised Jun 2026.
  • Handle: RePEc:arx:papers:2606.15740
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2606.15740
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lattimore, Pamela K. & Baker, Joanna R. & Witte, Ann D., 1992. "The influence of probability on risky choice: A parametric examination," Journal of Economic Behavior & Organization, Elsevier, vol. 17(3), pages 377-400, May.
    2. Christina McGranaghan & Kirby Nielsen & Ted O'Donoghue & Jason Somerville & Charles D. Sprenger, 2024. "Distinguishing Common Ratio Preferences from Common Ratio Effects Using Paired Valuation Tasks," American Economic Review, American Economic Association, vol. 114(2), pages 307-347, February.
    3. Christopher P. Chambers & Federico Echenique & Eran Shmaya, 2014. "The Axiomatic Structure of Empirical Content," American Economic Review, American Economic Association, vol. 104(8), pages 2303-2319, August.
    4. Machina, Mark J, 1987. "Choice under Uncertainty: Problems Solved and Unsolved," Journal of Economic Perspectives, American Economic Association, vol. 1(1), pages 121-154, Summer.
    5. Pavlo Blavatskyy, 2010. "Reverse common ratio effect," Journal of Risk and Uncertainty, Springer, vol. 40(3), pages 219-241, June.
    6. Bart Smeulders & Laurens Cherchye & Bram De Rock, 2021. "Nonparametric Analysis of Random Utility Models: Computational Tools for Statistical Testing," Econometrica, Econometric Society, vol. 89(1), pages 437-455, January.
    7. Nathaniel T. Wilcox, 2008. "Stochastic models for binary discrete choice under risk: a critical primer and econometric comparison," Research in Experimental Economics, in: Risk Aversion in Experiments, pages 197-292, Emerald Group Publishing Limited.
    8. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    9. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    10. John D. Hey, 2018. "Why We Should Not Be Silent About Noise," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 13, pages 309-329, World Scientific Publishing Co. Pte. Ltd..
    11. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    12. William J McCausland & Clintin Davis-Stober & AAJ Marley & Sanghyuk Park & Nicholas Brown, 2020. "Testing the Random Utility Hypothesis Directly," The Economic Journal, Royal Economic Society, vol. 130(625), pages 183-207.
    13. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2019. "What are axiomatizations good for?," Theory and Decision, Springer, vol. 86(3), pages 339-359, May.
    14. David S. Ahn & Todd Sarver, 2013. "Preference for Flexibility and Random Choice," Econometrica, Econometric Society, vol. 81(1), pages 341-361, January.
    15. Pavlo R. Blavatskyy, 2010. "Reverse Common Ratio Effect," IEW - Working Papers 478, Institute for Empirical Research in Economics - University of Zurich.
    16. Sendhil Mullainathan & Ashesh Rambachan, 2024. "From Predictive Algorithms to Automatic Generation of Anomalies," Papers 2404.10111, arXiv.org, revised Sep 2025.
    17. Pamela K. Lattimore & Joanna R. Baker & A. Dryden Witte, 1992. "The Influence Of Probability on Risky Choice: A parametric Examination," NBER Technical Working Papers 0081, National Bureau of Economic Research, Inc.
    18. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, vol. 74(1), pages 121-146, January.
    19. Pavlo Blavatskyy, 2007. "Stochastic expected utility theory," Journal of Risk and Uncertainty, Springer, vol. 34(3), pages 259-286, June.
    20. Ballinger, T Parker & Wilcox, Nathaniel T, 1997. "Decisions, Error and Heterogeneity," Economic Journal, Royal Economic Society, vol. 107(443), pages 1090-1105, July.
    21. 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.
    22. Turansick, Christopher, 2025. "An alternative approach for nonparametric analysis of random utility models," Journal of Economic Theory, Elsevier, vol. 226(C).
    23. Fishburn, Peter C., 1975. "Separation theorems and expected utilities," Journal of Economic Theory, Elsevier, vol. 11(1), pages 16-34, August.
    24. Graham Loomes, 2005. "Modelling the Stochastic Component of Behaviour in Experiments: Some Issues for the Interpretation of Data," Experimental Economics, Springer;Economic Science Association, vol. 8(4), pages 301-323, December.
    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. Liu Shi & Jianying Qiu & Jiangyan Li & Frank Bohn, 2024. "Consciously stochastic in preference reversals," Journal of Risk and Uncertainty, Springer, vol. 68(3), pages 255-297, June.
    2. Bernheim, B. Douglas & Sprenger, Charles, 2023. "On the empirical validity of cumulative prospect theory: A response to the Wakker commentaries," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 107(C).
    3. Wilcox, Nathaniel T., 2011. "'Stochastically more risk averse:' A contextual theory of stochastic discrete choice under risk," Journal of Econometrics, Elsevier, vol. 162(1), pages 89-104, May.
    4. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    5. Daniel Cavagnaro & Mark Pitt & Richard Gonzalez & Jay Myung, 2013. "Discriminating among probability weighting functions using adaptive design optimization," Journal of Risk and Uncertainty, Springer, vol. 47(3), pages 255-289, December.
    6. Blavatskyy, Pavlo, 2018. "Fechner’s strong utility model for choice among n>2 alternatives: Risky lotteries, Savage acts, and intertemporal payoffs," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 75-82.
    7. Blavatskyy, Pavlo, 2016. "Probability weighting and L-moments," European Journal of Operational Research, Elsevier, vol. 255(1), pages 103-109.
    8. Nathaniel T. Wilcox, 2015. "Error and Generalization in Discrete Choice Under Risk," Working Papers 15-11, Chapman University, Economic Science Institute.
    9. José Lara Resende & George Wu, 2010. "Competence effects for choices involving gains and losses," Journal of Risk and Uncertainty, Springer, vol. 40(2), pages 109-132, April.
    10. Pavlo Blavatskyy & Valentyn Panchenko & Andreas Ortmann, 2023. "How common is the common-ratio effect?," Experimental Economics, Springer;Economic Science Association, vol. 26(2), pages 253-272, April.
    11. Pavlo Blavatskyy, 2010. "Reverse common ratio effect," Journal of Risk and Uncertainty, Springer, vol. 40(3), pages 219-241, June.
    12. Chew, Soo Hong & Miao, Bin & Shen, Qiang & Zhong, Songfa, 2022. "Multiple-switching behavior in choice-list elicitation of risk preference," Journal of Economic Theory, Elsevier, vol. 204(C).
    13. Pavlo Blavatskyy, 2014. "Stronger utility," Theory and Decision, Springer, vol. 76(2), pages 265-286, February.
    14. Syngjoo Choi & Jeongbin Kim & Eungik Lee & Jungmin Lee, 2022. "Probability Weighting and Cognitive Ability," Management Science, INFORMS, vol. 68(7), pages 5201-5215, July.
    15. Uri Gneezy & Yoram Halevy & Brian Hall & Theo Offerman & Jeroen van de Ven, 2024. "How Real is Hypothetical? A High-Stakes Test of the Allais Paradox," Working Papers tecipa-783, University of Toronto, Department of Economics.
    16. Guo, Liang, 2021. "Contextual deliberation and the choice-valuation preference reversal," Journal of Economic Theory, Elsevier, vol. 195(C).
    17. Harrison, Glenn W., 2008. "Neuroeconomics: A Critical Reconsideration," Economics and Philosophy, Cambridge University Press, vol. 24(3), pages 303-344, November.
    18. George Wu & Alex B. Markle, 2008. "An Empirical Test of Gain-Loss Separability in Prospect Theory," Management Science, INFORMS, vol. 54(7), pages 1322-1335, July.
    19. Blavatskyy, Pavlo R., 2008. "Stochastic utility theorem," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1049-1056, December.
    20. Pavlo Blavatskyy, 2018. "A second-generation disappointment aversion theory of decision making under risk," Theory and Decision, Springer, vol. 84(1), pages 29-60, January.

    More about this item

    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:2606.15740. 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: https://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.