How causal reasoning can bias empirical evidence

How Causal Reasoning Can Bias Empirical Evidence Momme von Sydow 1 (momme.von-sydow@bio.uni-goettingen.de) York Hagmayer 1 (york.hagmayer@bio.uni-goettingen.de) Bjorn Meder 1,2 (meder@mpib-berlin.mpg.de) Michael R. Waldmann 1 (michael.waldmann@bio.uni-goettingen.de) Department of Psychology, University of Gottingen, Gosslerstr. 14, 37073 Gottingen, Germany Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany Abstract a) Chain Theories of causal reasoning and learning often implicitly as- sume that the structural implications of causal models and empirical evidence are consistent. However, for probabilistic causal relations this may not be the case. We propose a causal consistency hypothesis claiming that people tend to create consistency between the two types of knowledge. Mismatches between structural implications and empirical evidence may lead to distortions of empirical evidence. In the present re- search we used trial-by-trial learning tasks to study how people attempt to create consistency between structural as- sumptions and learning data. In Experiment 1 we show bias- ing of empirical evidence with causal chains even after re- peated testing of direct and indirect relations. Experiment 2 investigates whether different causal models lead to different judgments, despite identical data patterns. Overall, the find- ings support the idea that people try to reconcile assumptions about causal structure with probabilistic data, but also suggest that this may depend on the type of causal structure under consideration. b) CC C B A c) CE C B A C B A Figure 1: A causal chain, a common cause (CC) and a common effect (CE) model. Keywords: causal reasoning; induction; Markov condition; top-down effects; heuristics and biases Causal Reasoning and Empirical Evidence in Covariation Assessment Probability judgments about indirect causal relationships may be based on direct observations of covariations be- tween events (empirical evidence) or they may be derived from top-down assumptions about the underlying causal structure (structural knowledge). The crucial advantage of causal model knowledge is that we can make inferences about relations which we have not directly observed. For example, we may first learn about a causal relation A→B, and later about a causal relation B→C. By combining the single links into a causal chain A→B→C we can make infe- rences regarding the initial event A and the final event C. For example, deterministic causal relations warrant transi- tive inferences, that is, the occurrence of A allows us to infer that C is present, too (like in logical ‘Modus Barbara’). However, most causal relationships tend to be probabilistic: a virus does not always cause a disease; a gene does not always cause a phenotypic trait. Crucially, in the case of probabilistic relations, transitivity relations do not necessari- ly hold (see Ahn & Dennis, 2000; von Sydow, Meder, & Hagmayer, 2009). However, causal models may neverthe- less be used for assessing indirect relations from knowledge of direct relations, in a way that is inconsistent with direct empirical evidence. The representation of causal relationships in qualitative causal models (Gopnik et al., 2004; Rehder, 2003; Sloman, 2005; Waldmann, Hagmayer, & Blaisdell, 2006; Waldmann & Holyoak, 1992) and in causal Bayes nets (Pearl, 2000; Spirtes, Glymour, & Scheines, 1993) suggests that people only represent direct causal relations and infer other rela- tions from these causal models based on abstract assump- tions about the structures. At the center of the Bayes net for- malism is the causal Markov condition, which states that a variable in a causal network is conditionally independent of all other variables apart from its effects, given its direct causes. If the Markov condition holds, a causal chain (Fig. 1a) with positive direct relations, A B and B C, entails a positive contingency between variables A and C. More spe- cifically, the conditional probability of A given C, P(C|A), is given by: P(C|A) = P(B|A) ∙ P(C|B) + P( B|A) ∙ P(C| B) Similarly, other indirect conditional probabilities can be derived from applying the Markov condition to the causal model. If we have a common cause model (CC, cf. Fig. 1b) A B C, the Bayes net formalism implies a positive rela- tion between A and C. On the other hand, if the variables are linked in a common effect structure A B C (CE, cf. Fig. 1c), no positive relation between A and C is entailed. From a computational point of view, the Markov assump- tion is used as prerequisite for inducing causal structures from conditional dependency and independency relations, and as a basis for probabilistic inferences across complex causal networks (Spirtes et al., 1993; Pearl, 2000). On the other hand, the status of the Markov condition as a neces- sary and universal feature of causal representations has been criticized (Cartwright, 2001). However,, the status of the Markov condition in human causal reasoning is still under dispute (e.g., Rehder & Burnett, 2005; Mayrhofer, Good- man, Tenenbaum, & Waldmann, 2008).