IDEAS home Printed from https://ideas.repec.org/p/aut/wpaper/201806.html
   My bibliography  Save this paper

Stochastic Expected Utility for Binary Choice: New Representations

Author

Listed:
  • Matthew Ryan

    (School of Economics, 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 strictly (Ryan 2018a) and simply (Tversky and Russo, 1969) scalable models, plus strict (Ryan, 2015) and strong (Debreu, 1958) Fechner models. Our axiomatisations complement the important contributions of Blavatskyy (2008) and Dagsvik (2008). Our representation theorems set all models on a common axiomatic foundation, progressively augmented by additional axioms necessary to characterise successively more restrictive models. In particular, we are able to decompose Blavatskyy's (2008) common consequence independence axiom into two parts: one that underwrites the linearity of utility and another than underwrites the Fechnerian structure of noise. This has signifcant advantages for testing the Fechnerian models, as we discuss.

Suggested Citation

  • Matthew Ryan, 2018. "Stochastic Expected Utility for Binary Choice: New Representations," Working Papers 2018-06, Auckland University of Technology, Department of Economics.
    • Handle: RePEc:aut:wpaper:201806
    as

    Download full text from publisher

    File URL: https://www.aut.ac.nz/__data/assets/pdf_file/0006/188727/Economics-WP-2018-06.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. John D. Hey, 2018. "Experimental investigations of errors in decision making under risk," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 17, pages 381-388, World Scientific Publishing Co. Pte. Ltd..
    2. Dagsvik, John K., 2008. "Axiomatization of stochastic models for choice under uncertainty," Mathematical Social Sciences, Elsevier, vol. 55(3), pages 341-370, May.
    3. 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.
    4. Blavatskyy, Pavlo R., 2008. "Stochastic utility theorem," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1049-1056, December.
    5. Fishburn, P.C., 1984. "SSB Utility theory: an economic perspective," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 63-94, August.
    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, 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.
    2. 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.
    3. Pavlo R. Blavatskyy, 2011. "A Model of Probabilistic Choice Satisfying First-Order Stochastic Dominance," Management Science, INFORMS, vol. 57(3), pages 542-548, March.
    4. 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.
    5. Blavatskyy, Pavlo, 2016. "Probability weighting and L-moments," European Journal of Operational Research, Elsevier, vol. 255(1), pages 103-109.
    6. Matthew Ryan, 2015. "A Strict Stochastic Utility Theorem," Economics Bulletin, AccessEcon, vol. 35(4), pages 2664-2672.
    7. Pavlo Blavatskyy, 2014. "Stronger utility," Theory and Decision, Springer, vol. 76(2), pages 265-286, February.
    8. 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.
    9. Guido Baltussen & G. Post & Martijn Assem & Peter Wakker, 2012. "Random incentive systems in a dynamic choice experiment," Experimental Economics, Springer;Economic Science Association, vol. 15(3), pages 418-443, September.
    10. 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.
    11. Blavatskyy, Pavlo R., 2012. "Utility of a quarter-million," Economics Letters, Elsevier, vol. 117(3), pages 650-653.
    12. 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.
    13. Matthew Ryan, 2015. "Binary Choice Probabilities on Mixture Sets," Working Papers 2015-01, Auckland University of Technology, Department of Economics.
    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. Despoina Alempaki & Emina Canic & Timothy L. Mullett & William J. Skylark & Chris Starmer & Neil Stewart & Fabio Tufano, 2019. "Reexamining How Utility and Weighting Functions Get Their Shapes: A Quasi-Adversarial Collaboration Providing a New Interpretation," Management Science, INFORMS, vol. 65(10), pages 4841-4862, October.
    16. 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.
    17. Addison Pan, 2022. "Empirical tests of stochastic binary choice models," Theory and Decision, Springer, vol. 93(2), pages 259-280, September.
    18. Blavatskyy, Pavlo, 2013. "Which decision theory?," Economics Letters, Elsevier, vol. 120(1), pages 40-44.
    19. Blavatskyy, Pavlo, 2019. "Future plans and errors," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 85-92.
    20. Blavatskyy, Pavlo, 2015. "Behavior in the centipede game: A decision-theoretical perspective," Economics Letters, Elsevier, vol. 133(C), pages 117-122.

    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:aut:wpaper:201806. 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: Gail Pacheco (email available below). General contact details of provider: https://edirc.repec.org/data/fbautnz.html .

    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.