IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v72y2021i2d10.1007_s00199-020-01307-8.html
   My bibliography  Save this article

Stochastic expected utility for binary choice: a ‘modular’ axiomatic foundation

Author

Listed:
  • Matthew Ryan

    (Auckland University of Technology)

Abstract

We present new axiomatisations for various models of binary stochastic choice that may be characterised as “expected utility maximisation with noise”. These include axiomatisations of simple scalability (Tversky and Russo in J Math Psychol 6:1–12, 1969) with respect to a scale having the expected utility (EU) form, and strong utility (Debreu in Econometrica 26(3):440–444, 1958) of the EU form. The latter model features Fechnerian “noise”: choice probabilities depend on EU differences. Our axiomatisations complement the important contributions of Blavatskyy (J Math Econ 44:1049–1056, 2008) and Dagsvik (Math Soc Sci 55:341–370, 2008). Our representation theorems set all models on a common axiomatic foundation, with additional axioms added in modular fashion to characterise successively more restrictive models. The key is a decomposition of Blavatskyy’s (2008) common consequence independence axiom into two parts: one (which we call weak independence) that underwrites the EU form of utility and another (stochastic symmetry) than underwrites the Fechnerian structure of noise. We also show that in many cases of interest (which we call preference-bounded domains) stochastic symmetry can be replaced with weak transparent dominance (WTD). For choice between lotteries, WTD only restricts behaviour when choosing between probability mixtures of a “best” and a “worst” possible outcome.

Suggested Citation

  • Matthew Ryan, 2021. "Stochastic expected utility for binary choice: a ‘modular’ axiomatic foundation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 641-669, September.
    • Handle: RePEc:spr:joecth:v:72:y:2021:i:2:d:10.1007_s00199-020-01307-8
    DOI: 10.1007/s00199-020-01307-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-020-01307-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-020-01307-8?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Pavlo R. Blavatskyy, 2011. "A Model of Probabilistic Choice Satisfying First-Order Stochastic Dominance," Management Science, INFORMS, vol. 57(3), pages 542-548, March.
    2. Dagsvik, John K., 2015. "Stochastic models for risky choices: A comparison of different axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 81-88.
    3. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, vol. 74(1), pages 121-146, January.
    4. Blavatskyy, Pavlo R., 2008. "Stochastic utility theorem," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1049-1056, December.
    5. Matthew Ryan, 2010. "Mixture sets on finite domains," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(2), pages 139-147, November.
    6. Dagsvik, John K., 2008. "Axiomatization of stochastic models for choice under uncertainty," Mathematical Social Sciences, Elsevier, vol. 55(3), pages 341-370, May.
    7. Matthew Ryan, 2017. "Random Binary Choices that Satisfy Stochastic Betweenness," Working Papers 2017-01, Auckland University of Technology, Department of Economics.
    8. Birnbaum, Michael H & Navarrete, Juan B, 1998. "Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence," Journal of Risk and Uncertainty, Springer, vol. 17(1), pages 49-78, October.
    9. Pavlo R. Blavatskyy & Ganna Pogrebna, 2010. "Models of stochastic choice and decision theories: why both are important for analyzing decisions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(6), pages 963-986.
    10. Henry Stott, 2006. "Cumulative prospect theory's functional menagerie," Journal of Risk and Uncertainty, Springer, vol. 32(2), pages 101-130, March.
    11. Ryan, Matthew, 2017. "Random binary choices that satisfy stochastic betweenness," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 176-184.
    12. Matthew Ryan, 2015. "A Strict Stochastic Utility Theorem," Economics Bulletin, AccessEcon, vol. 35(4), pages 2664-2672.
    13. 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.
    14. Fishburn, P.C., 1984. "SSB Utility theory: an economic perspective," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 63-94, August.
    15. Pavlo Blavatskyy, 2012. "Probabilistic choice and stochastic dominance," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 59-83, May.
    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. Matthew Ryan, 2018. "Uncertainty and binary stochastic choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(3), pages 629-662, May.
    2. Dagsvik, John K., 2015. "Stochastic models for risky choices: A comparison of different axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 81-88.
    3. Matthew Ryan, 2020. "Reconciling dominance and stochastic transitivity in random binary choice," Working Papers 2020-05, Auckland University of Technology, Department of Economics.
    4. Michael H. Birnbaum & Ulrich Schmidt & Miriam D. Schneider, 2017. "Testing independence conditions in the presence of errors and splitting effects," Journal of Risk and Uncertainty, Springer, vol. 54(1), pages 61-85, February.
    5. Pavlo Blavatskyy, 2018. "A Refinement of Logit Quantal Response Equilibrium," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-14, June.
    6. Daniel Navarro-Martinez & Graham Loomes & Andrea Isoni & David Butler & Larbi Alaoui, 2018. "Boundedly rational expected utility theory," Journal of Risk and Uncertainty, Springer, vol. 57(3), pages 199-223, December.
    7. Matthew Ryan, 2018. "Stochastic Expected Utility for Binary Choice: New Representations," Working Papers 2018-06, Auckland University of Technology, Department of Economics.
    8. Addison Pan, 2022. "Empirical tests of stochastic binary choice models," Theory and Decision, Springer, vol. 93(2), pages 259-280, September.
    9. Blavatskyy, Pavlo, 2016. "Probability weighting and L-moments," European Journal of Operational Research, Elsevier, vol. 255(1), pages 103-109.
    10. Blavatskyy, Pavlo, 2013. "Which decision theory?," Economics Letters, Elsevier, vol. 120(1), pages 40-44.
    11. Pavlo Blavatskyy, 2021. "Probabilistic independence axiom," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 46(1), pages 21-34, March.
    12. Blavatskyy, Pavlo, 2015. "Behavior in the centipede game: A decision-theoretical perspective," Economics Letters, Elsevier, vol. 133(C), pages 117-122.
    13. Pavlo Blavatskyy, 2014. "Stronger utility," Theory and Decision, Springer, vol. 76(2), pages 265-286, February.
    14. Dagsvik, John K., 2018. "Invariance axioms and functional form restrictions in structural models," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 85-95.
    15. Dino Borie, 2016. "Expected Multi-Utility Representations by "Simplex" with Applications," GREDEG Working Papers 2016-10, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    16. 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.
    17. Pavlo R. Blavatskyy, 2020. "Dual choice axiom and probabilistic choice," Journal of Risk and Uncertainty, Springer, vol. 61(1), pages 25-41, August.
    18. Ryan, Matthew, 2017. "Random binary choices that satisfy stochastic betweenness," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 176-184.
    19. Pavlo R. Blavatskyy, 2011. "A Model of Probabilistic Choice Satisfying First-Order Stochastic Dominance," Management Science, INFORMS, vol. 57(3), pages 542-548, March.
    20. Blavatskyy, Pavlo, 2019. "Future plans and errors," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 85-92.

    More about this item

    Keywords

    Stochastic choice; Expected utility; Scalability; Fechner;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:spr:joecth:v:72:y:2021:i:2:d:10.1007_s00199-020-01307-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.