Abstract
Causal reasoning is crucial to people’s decision making in probabilistic environments. It may rely directly on data about covariation between variables (correspondence) or on inferences based on reasonable constraints if larger causal models are constructed based on local relations (coherence). For causal chains an often assumed constraint is transitivity. For probabilistic causal relations, mismatches between such transitive inferences and direct empirical evidence may lead to distortions of empirical evidence. Previous work has shown that people may use the generative local causal relations A → B and B → C to infer a positive indirect relation between events A and C, despite data showing that these events are actually independent (von Sydow et al. in Proceedings of the thirty-first annual conference of the cognitive science society. Cognitive Science Society, Austin, 2009, Proceedings of the 32nd annual conference of the cognitive science society. Cognitive Science Society, Austin, 2010, Mem Cogn 44(3):469–487, 2016). Here we used a sequential learning scenario to investigate how transitive reasoning in intransitive situations with negatively related distal events may relate to betting behavior. In three experiments participants bet as if they were influenced by a transitivity assumption, even when the data strongly contradicted transitivity.
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Although normal distribution was violated within conditions we still report the results of parametric tests as they have proven to be robust against this deviation. In all cases analyses using nonparametric tests led to comparable results to those reported.
Note that although the shown data for A and D exactly correspond to ΔP AD = .5, ΔP AD = −.5, the product of local ΔPs is not .5, but .55. Therefore, the chain presented in the global-transitive group slightly differs from a perfectly transitive chain. This is due to the omission of very rare cases that a transitive chain produces. This was necessary to keep learning trials at a reasonable number.
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Acknowledgements
We are grateful to Shirin Betzler, Julia Folz, Alina Greis, Kamala Grothe, Vera Hampel, Antonia Lange, and Alexander Wendt for their valuable work during data collection. Portions of Experiments 1 and 2 were presented at the 2014 Cognitive Science conference in Quebec, Canada (Hebbelmann and von Sydow 2014). This research and the empirical studies were supported by the Grant Sy 111/2 to Momme von Sydow from the Deutsche Forschungsgemeinschaft (DFG) as part of the priority program New Frameworks of Rationality (SPP 1516) as well as the DFG Grant FI294/23 to Klaus Fiedler.
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Handling editor: Don Ross (University of Cape Town); Reviewers: Harold Kincaid (University of Cape Town), Benjamin Rottman (University of Pittsburgh).
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Hebbelmann, D., von Sydow, M. Betting on transitivity in probabilistic causal chains. Cogn Process 18, 505–519 (2017). https://doi.org/10.1007/s10339-017-0821-x
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DOI: https://doi.org/10.1007/s10339-017-0821-x