IDEAS home Printed from https://ideas.repec.org/p/aut/wpaper/201701.html
   My bibliography  Save this paper

Random Binary Choices that Satisfy Stochastic Betweenness

Author

Listed:
  • Matthew Ryan

    (School of Economics, Faculty of Business and Law, Auckland University of Technology)

Abstract

Experimental evidence suggests that the process of choosing between lotteries (risky prospects) is stochastic and is better described through choice probabilities than preference relations. Binary choice probabilities admit a Fechner representation if there exists a utility function u such that the probability of choosing a over b is a non-decreasing function of the utility di¤erence u (a) - u (b). The representation is strict if u (a) u (b) precisely when the decision-maker is at least as likely to choose a from fa; bg as to choose b. Blavatskyy (2008) obtained necessary and su¢ cient conditions for a strict Fechner representation in which u has the expected utility form. One of these is the common consequence independence (CCI) axiom (ibid.,Axiom 4), which is a stochastic analogue of the mixture independence condition on preferences. Blavatskyy also conjectured that by weakening CCI to a condition he called stochastic betweenness (SB) stochastic analogue of the betweenness condition on preferen-ces (Chew (1983)) - one obtains necessary and suffcient conditions for a strict Fechner representation in which u has the implicit expected utility form (Dekel (1986)). We show that Blavatskyys conjecture is false, and provide a valid set of necessary and su¢ cient conditions for the desired representation.

Suggested Citation

  • Matthew Ryan, 2017. "Random Binary Choices that Satisfy Stochastic Betweenness," Working Papers 2017-01, Auckland University of Technology, Department of Economics.
  • Handle: RePEc:aut:wpaper:201701
    as

    Download full text from publisher

    File URL: https://www.aut.ac.nz/__data/assets/pdf_file/0007/107881/Economics-WP-2017-01.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dagsvik, John K., 2008. "Axiomatization of stochastic models for choice under uncertainty," Mathematical Social Sciences, Elsevier, vol. 55(3), pages 341-370, May.
    2. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    3. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
    4. Frederick Mosteller & Philip Nogee, 1951. "An Experimental Measurement of Utility," Journal of Political Economy, University of Chicago Press, vol. 59(5), pages 371-371.
    5. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Matthew Ryan, 2020. "Reconciling dominance and stochastic transitivity in random binary choice," Working Papers 2020-05, Auckland University of Technology, Department of Economics.
    2. 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.
    3. Addison Pan, 2022. "Empirical tests of stochastic binary choice models," Theory and Decision, Springer, vol. 93(2), pages 259-280, September.

    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. Ryan, Matthew, 2017. "Random binary choices that satisfy stochastic betweenness," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 176-184.
    2. 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.
    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. Uzi Segal, 2021. "For all or exists?," Boston College Working Papers in Economics 1034, Boston College Department of Economics.
    6. Kemal Ozbek, 2024. "Expected utility, independence, and continuity," Theory and Decision, Springer, vol. 97(1), pages 1-22, August.
    7. Bikhchandani, Sushil & Segal, Uzi, 2014. "Transitive regret over statistically independent lotteries," Journal of Economic Theory, Elsevier, vol. 152(C), pages 237-248.
    8. Raquel M. Gaspar & Paulo M. Silva, 2023. "Investors’ perspective on portfolio insurance," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 22(1), pages 49-79, January.
    9. Soham R. Phade & Venkat Anantharam, 2020. "Black-Box Strategies and Equilibrium for Games with Cumulative Prospect Theoretic Players," Papers 2004.09592, arXiv.org.
    10. Simon Grant & John Quiggin, 2005. "Learning and Discovery," Risk & Uncertainty Working Papers WP7R05, Risk and Sustainable Management Group, University of Queensland.
    11. Yusufcan Masatlioglu & Collin Raymond, 2016. "A Behavioral Analysis of Stochastic Reference Dependence," American Economic Review, American Economic Association, vol. 106(9), pages 2760-2782, September.
    12. Latifa Ghalayini & Dana Deeb, 2021. "Utility Measurement in Integrative Negotiation," Information Management and Business Review, AMH International, vol. 13(1), pages 1-15.
    13. Gayer, Gabrielle, 2010. "Perception of probabilities in situations of risk: A case based approach," Games and Economic Behavior, Elsevier, vol. 68(1), pages 130-143, January.
    14. Michele Bernasconi, 2002. "How should income be divided? questionnaire evidence from the theory of “Impartial preferences”," Journal of Economics, Springer, vol. 9(1), pages 163-195, December.
    15. Thibault Gajdos & Feriel Kandil, 2008. "The ignorant observer," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 193-232, August.
    16. Kontek, Krzysztof, 2015. "Fanning-Out or Fanning-In? Continuous or Discontinuous? Estimating Indifference Curves Inside the Marschak-Machina Triangle using Certainty Equivalents," MPRA Paper 63965, University Library of Munich, Germany.
    17. Zvi Safra & Uzi Segal, 2005. "Are Universal Preferences Possible? Calibration Results for Non-Expected Utility Theories," Boston College Working Papers in Economics 633, Boston College Department of Economics.
    18. Bin Miao & Songfa Zhong, 2018. "Probabilistic social preference: how Machina’s Mom randomizes her choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(1), pages 1-24, January.
    19. Bernasconi, Michele, 1992. "Different Frames for the Independence Axiom: An Experimental Investigation in Individual Decision Making under Risk," Journal of Risk and Uncertainty, Springer, vol. 5(2), pages 159-174, May.
    20. Mongin, Philippe & Pivato, Marcus, 2015. "Ranking multidimensional alternatives and uncertain prospects," Journal of Economic Theory, Elsevier, vol. 157(C), pages 146-171.

    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:201701. 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.