The Bayesian logic of frequency-based conjunction fallacies

Sydow, Momme von

doi:10.1016/j.jmp.2010.12.001

Cited by 14 publications

(13 citation statements)

References 99 publications

(190 reference statements)

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“…According to Bayes nets, causal chains and common-cause structures are BMarkov equivalent.^This suggests identical inferential distortion effects for both structures. Empirically, however, the evidence on the direct psychological validity of the Markov condition for common-cause structures is mixed (Rehder & Burnett, 2005; see also Jarecki et al, 2013;Mayrhofer, Goodman, Waldmann, & Tenenbaum, 2008;Mayrhofer & Waldmann, 2015;Rottman & Hastie, 2013;von Sydow, 2011von Sydow, , 2013. Future research should compare reasoning with different causal structures when the data violate the Markov assumption .…”

Section: Contingency Conditionmentioning

confidence: 99%

Transitive reasoning distorts induction in causal chains

2015

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A probabilistic causal chain A→B→C may intuitively appear to be transitive: If A probabilistically causes B, and B probabilistically causes C, A probabilistically causes C. However, probabilistic causal relations can only guaranteed to be transitive if the so-called Markov condition holds. In two experiments, we examined how people make probabilistic judgments about indirect relationships A→C in causal chains A→B→C that violate the Markov condition. We hypothesized that participants would make transitive inferences in accordance with the Markov condition although they were presented with counterevidence showing intransitive data. For instance, participants were successively presented with data entailing positive dependencies A→B and B→C. At the same time, the data entailed that A and C were statistically independent. The results of two experiments show that transitive reasoning via a mediating event B influenced and distorted the induction of the indirect relation between A and C. Participants' judgments were affected by an interaction of transitive, causalmodel-based inferences and the observed data. Our findings support the idea that people tend to chain individual causal relations into mental causal chains that obey the Markov condition and thus allow for transitive reasoning, even if the observed data entail that such inferences are not warranted. Transitive reasoning enables judgments about unobserved relationships based on indirect evidence. If one observes that object A is heavier than object B, and that B is heavier than C, one can infer that A is heavier than C. Not all relations, however, are transitive. If A is the mother of B, and B is the mother of C, this does not mean that A is the mother of C.We investigate whether and to what extent people reason transitively about causal relations, even when the conditions for transitive inferences do not hold true. We focus on probabilistic causal chains of the type A→B→C, where individual relations A→B and B→C can be combined to form a chain A→B→C to make probabilistic inferences from the chain's initial event A to the terminal event C. First, we specify the conditions under which transitive reasoning in causal chains is valid. We then report the findings of two experiments investigating whether people make transitive inferences even when the available data entail that such inferences are not warranted.Our research builds on the idea that people represent the world in terms of mental causal models (

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Section: Contingency Conditionmentioning

confidence: 99%

Transitive reasoning distorts induction in causal chains

2015

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“…This argument is supported in different research areas, for instance, consumer researchers have concluded from a substantial body of studies that people's choices are more reliable than their absolute evaluations of choice options (e.g., Adamowicz, Boxall, Williams, & Louviere, 1998). Eurther, statistical task structures (e.g.. Shanks & Lagnado, 2002;von Sydow, 2011) have the advantage in that they do not require the specification of ideal logical sets using normal language. Examining people's choices between conjunctive probability options instead of people's probability judgments also represents a novel contribution of the present work, because to our knowledge choice tasks have only been used in "verbal studies" so far.…”

Section: Models Of Probability Judgmentmentioning

confidence: 99%

Inferring conjunctive probabilities from noisy samples: Evidence for the configural weighted average model.

Jenny¹,

Rieskamp²,

Nilsson³

2014

Journal of Experimental Psychology: Learning, Memory, and Cogni

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Judging whether multiple events will co-occur is an important aspect of everyday decision making. The underlying probabilities of occurrence are usually unknown and have to be inferred from experience. Using a rigorous, quantitative model comparison, we investigate how people judge the conjunctive probabilities of multiple events to co-occur. In 2 experiments, participants had to repeatedly choose between pairs of 2 conjunctive events (represented as 2 gambles). To estimate the probability that both events occur, they had access to a small sample of information. The 1st experiment consisted of a balanced set of gambles, whereas in the 2nd experiment, the gambles were constructed such that the models maximally differed in their predictions. A hierarchical Bayesian approach used for estimating the models' parameters and for testing the models against each other showed that the majority of participants were best described by the configural weighted average model. This model performed best in predicting people's choices, and it assumes that constituent probabilities are ranked by importance, weighted accordingly, and added up. The cognitive modeling approach provides an understanding of the cognitive processes underlying people's conjunctive probability judgments.

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“…(Step 6), it assigns probabilities to these propositions as a whole (cf. Foley 2009, von Sydow 2011.…”

Section: Bayesian Mental Model Approach Of Conditionals (Bmmc)mentioning

confidence: 99%

“…This links to the debate concerning conjunction fallacies and other inclusion fallacies (given p, 'q_non-q' refers to the tautology and includes the affirmation q; cf. von Sydow 2011Sydow , 2014.…”

Section: Bayesian Mental Model Approach Of Conditionals (Bmmc)mentioning

confidence: 99%