IDEAS home Printed from https://ideas.repec.org/a/taf/nzecpp/v45y2011i1-2p195-207.html
   My bibliography  Save this article

Ambiguity, the certainty illusion, and the natural frequency approach to reasoning with inverse probabilities

Author

Listed:
  • John Fountain
  • Philip Gunby

Abstract

People have difficulty reasoning with diagnostic information in uncertain situations, especially when an understanding and calculation of inverse conditional probabilities (Bayes theorem) is required. While natural frequency representations of inference tasks improve matters, they suffer from three problems: (1) calculation errors persist with a majority of subjects; (2) the representation suffers from an illusion of certainty that ignores ambiguity; and (3) the costs of repeatedly applying the representation to deal with imprecision and ambiguity in inference are prohibitive. We describe a user friendly, interactive, graphical software tool for calculating, visualizing, and communicating accurate inferences about uncertain states when relevant diagnostic test information (sensitivity, specificity, and base rate) is both imperfect and ambiguous in its application to a specific patient. The software is free, open-source, and runs on all popular PC operating systems (Windows, Mac, Linux).

Suggested Citation

  • John Fountain & Philip Gunby, 2011. "Ambiguity, the certainty illusion, and the natural frequency approach to reasoning with inverse probabilities," New Zealand Economic Papers, Taylor & Francis Journals, vol. 45(1-2), pages 195-207.
    • Handle: RePEc:taf:nzecpp:v:45:y:2011:i:1-2:p:195-207
    DOI: 10.1080/00779954.2011.556079
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/00779954.2011.556079
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00779954.2011.556079?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. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    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. Fujikawa, Takemi, 2009. "The hot stove effect in repeated-play decision making under ambiguity," MPRA Paper 17647, University Library of Munich, Germany.
    2. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    3. Peter John Robinson & W. J. Wouter Botzen & Fujin Zhou, 2021. "An experimental study of charity hazard: The effect of risky and ambiguous government compensation on flood insurance demand," Journal of Risk and Uncertainty, Springer, vol. 63(3), pages 275-318, December.
    4. Gajdos, Thibault & Maurin, Eric, 2004. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," Journal of Economic Theory, Elsevier, vol. 116(1), pages 93-118, May.
    5. Luca De Gennaro Aquino & Sascha Desmettre & Yevhen Havrylenko & Mogens Steffensen, 2024. "Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time," Papers 2407.16525, arXiv.org, revised Oct 2024.
    6. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    7. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    8. ,, 2014. "Second order beliefs models of choice under imprecise risk: non-additive second order beliefs vs. nonlinear second order utility," Theoretical Economics, Econometric Society, vol. 9(3), September.
    9. James K. Hammitt, 2020. "Valuing mortality risk in the time of COVID-19," Journal of Risk and Uncertainty, Springer, vol. 61(2), pages 129-154, October.
    10. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    11. Armantier, Olivier & Treich, Nicolas, 2013. "Eliciting beliefs: Proper scoring rules, incentives, stakes and hedging," European Economic Review, Elsevier, vol. 62(C), pages 17-40.
    12. Baker, Erin & Bosetti, Valentina & Salo, Ahti, 2016. "Finding Common Ground when Experts Disagree: Belief Dominance over Portfolios of Alternatives," MITP: Mitigation, Innovation and Transformation Pathways 243147, Fondazione Eni Enrico Mattei (FEEM).
    13. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    14. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    15. Hippolyte d’Albis & Emmanuel Thibault, 2018. "Ambiguous life expectancy and the demand for annuities," Theory and Decision, Springer, vol. 85(3), pages 303-319, October.
    16. Jingyi Xue, 2020. "Preferences with changing ambiguity aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 1-60, February.
    17. repec:esx:essedp:770 is not listed on IDEAS
    18. Amarante, Massimiliano & Ghossoub, Mario & Phelps, Edmund, 2015. "Ambiguity on the insurer’s side: The demand for insurance," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 61-78.
    19. Gérard Mondello, 2022. "Information Source's Reliability," GREDEG Working Papers 2022-21, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France, revised Oct 2022.
    20. Mohammed Abdellaoui & Peter Klibanoff & Lætitia Placido, 2015. "Experiments on Compound Risk in Relation to Simple Risk and to Ambiguity," Management Science, INFORMS, vol. 61(6), pages 1306-1322, June.
    21. Emmanuel Kemel & Muriel Travers, 2016. "Comparing attitudes toward time and toward money in experience-based decisions," Theory and Decision, Springer, vol. 80(1), pages 71-100, January.

    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:taf:nzecpp:v:45:y:2011:i:1-2:p:195-207. 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: the person in charge (email available below). General contact details of provider: http://www.tandfonline.com/RNZP20 .

    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.