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  • ACTA UNIVERSITATIS

    UPSALIENSIS UPPSALA

    2019

    Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences 166

    The Cognitive Basis of Joint Probability Judgments

    Processes, Ecology, and Adaption

    JOAKIM SUNDH

    ISSN 1652-9030 ISBN 978-91-513-0608-7 urn:nbn:se:uu:diva-380099

  • Dissertation presented at Uppsala University to be publicly examined in Humanistiska teatern, Engelska parken, Thunbergsv. 3H, Uppsala, Monday, 20 May 2019 at 10:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Jörg Rieskamp (University of Basel, Faculty of Psychology).

    Abstract Sundh, J. 2019. The Cognitive Basis of Joint Probability Judgments. Processes, Ecology, and Adaption. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences 166. 60 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-513-0608-7.

    When navigating an uncertain world, it is often necessary to judge the probability of a conjunction of events, that is, their joint probability. The subject of this thesis is how people infer joint probabilities from probabilities of individual events. Study I explored such joint probability judgment tasks in conditions with independent events and conditions with systematic risk that could be inferred through feedback. Results indicated that participants tended to approach the tasks using additive combinations of the individual probabilities, but switch to multiplication (or, to a lesser extent, exemplar memory) when events were independent and additive strategies therefore were less accurate. Consequently, participants were initially more accurate in the task with high systematic risk, despite that task being more complex from the perspective of probability theory. Study II simulated the performance of models of joint probability judgment in tasks based both on computer generated data and real-world data-sets, to evaluate which cognitive processes are accurate in which ecological contexts. Models used in Study I and other models inspired by current research were explored. The results confirmed that, by virtue of their robustness, additive models are reasonable general purpose algorithms, although when one is familiar with the task it is preferable to switch to other strategies more specifically adapted to the task. After Study I found that people adapt strategy choice according to dependence between events and Study II confirmed that these adaptions are justified in terms of accuracy, Study III investigated whether adapting to stochastic dependence implied thinking according to stochastic principles. Results indicated that this was not the case, but that participants instead worked according to the weak assumption that events were independent, regardless of the actual state of the world. In conclusion, this thesis demonstrates that people generally do not combine individual probabilities into joint probability judgments in ways consistent with the basic principles of probability theory or think of the task in such terms, but neither does there appear to be much reason to do so. Rather, simpler heuristics can often approximate equally or more accurate judgments.

    Keywords: Judgment and decision-making, Joint probability judgment, Probability theory, Ecological rationality

    Joakim Sundh, Department of Psychology, Box 1225, Uppsala University, SE-75142 Uppsala, Sweden.

    © Joakim Sundh 2019

    ISSN 1652-9030 ISBN 978-91-513-0608-7 urn:nbn:se:uu:diva-380099 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-380099)

  • “I failed math twice, never fully grasping probability theory. I mean,

    first off, who cares if you pick a black ball or a white ball out of the

    bag? And second, if you’re bent over about the color, don’t leave it to

    chance. Look in the damn bag and pick the color you want.”

    - Janet Evanovich

  • List of Papers

    This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

    I Sundh, J., & Juslin, P. (2018). Compound risk judgment in

    tasks with both idiosyncratic and systematic risk: The “Robust Beauty” of additive probability integration. Cognition, 171, 25– 41

    II Sundh, J. (2019). The ecological scopes of cognitive models for joint probability judgment. Manuscript.

    III Sundh, J., Juslin, P., & Millroth, P. (2019). Appreciation for in- dependence: Does adaptation to stochastic dependence imply thinking according to stochastic principles?. Manuscript.

    Reprints were made with permission from the respective publishers. For all studies included in this thesis, Joakim Sundh planned and designed the experiments, analyzed the data, and wrote the manuscripts, along with contributions to all aforementioned areas from supervisor and, where appli- cable, co-authors.

  • Contents

    Introduction ..................................................................................................... 9 

    Probability Theory and the Human Mind ..................................................... 11  The Rational Animal ................................................................................ 11  Heuristics and Biases ............................................................................... 12  Correspondence and Linear Models ......................................................... 13  Ecological Rationality and the Adaptive Toolbox ................................... 15  The Bayesian Brain .................................................................................. 17  Summary .................................................................................................. 17 

    Probability Theory and the External World .................................................. 19  Small samples ........................................................................................... 19  Dependence .............................................................................................. 20  Generative Models ................................................................................... 21  Summary .................................................................................................. 22 

    Joint Probability Judgment ........................................................................... 23 

    Cognitive Resources: Reasoning, Intuitive Judgment, and Memory ............ 25 

    Aims .............................................................................................................. 28 

    Study I ........................................................................................................... 29  Background .............................................................................................. 29  Experiment I ............................................................................................. 30 

    Methods ............................................................................................... 30  Results ................................................................................................. 31 

    Experiment II ............................................................................................ 32  Methods ............................................................................................... 32  Results ................................................................................................. 33 

    Experiment III .......................................................................................... 33  Methods ............................................................................................... 33  Results ................................................................................................. 33 

    Conclusions .............................................................................................. 34 

    Study II ......................................................................................................... 35  Background .............................................................................................. 35  Methods .................................................................................................... 35 

  • Results ...................................................................................................... 36  Conclusions .............................................................................................. 41 

    Study III ........................................................................................................ 42  Background .............................................................................................. 42  Experiment I ............................................................................................. 42 

    Methods ............................................................................................... 42  Results ................................................................................................. 43 

    Experiment II ............................................................................................ 44  Methods ............................................................................................... 44  Results ................................................................................................. 45 

    Conclusions .............................................................................................. 46 

    General Discussion .....................................