Evaluating Causal Hypotheses: The Curious Case of Correlated Cues

Although the causal graphical model framework has achieved considerable success accounting for causal learning data, application of that formalism to multi-cause situations assumes that people are insensitive to the statistical properties of the causes themselves. The present experiment tests this assumption by first instructing subjects on a causal model consisting of two independent and generative causes and then requesting them to make data likelihood judgments, that is, to estimate the probability of some data given the model. The correlation between the causes in the data was either positive, zero, or negative. The data was judged as most likely in the positive condition and least likely in the negative condition, a finding that obtained even though all other statistical properties of the data (e.g., causal strengths, outcome density) were controlled. These results pose a problem for current models of causal learning. Hypothesis testing occupies a central role in learning theory. On this view, learners use observed data to update their beliefs about different possible models of the world. A critical component of this process are learners’ judgments regarding how probable, or improbable, it is that the observed data were generated by each of the hypotheses. In this paper we consider what factors affect learner’s judgments regarding the likelihood that data was generated a particular causal hypothesis. For example, consider the situation where there are two potential causes (C! and C!) of an effect E. Fig. 1 shows the four hypotheses, or graphs (G), formed by crossing the presence/absence of C! → E with the presence/absence of C! → E. Evaluating the posterior probability of these graphs involves calculating the probability of the observations, or the data (D), were generated by each graph, p(D|G!), and then applying Bayes’ law. Indeed, Carroll, Cheng, and Lu (2013) adopted the hypothesis testing framework shown in Fig. 1 to account for learning data from some traditional associative learning paradigms involving two cues. While Griffiths and Tenenbaum (2005) initially developed the hypothesis testing methodology to account for learning data from simpler situations involving just one potential cause (also see Lu et al., 2008; Meder et al., 2014), it has since been extended to multi-cause situations (e.g., three potential causes in Powell et al., 2016). Our purpose in this article is to highlight what we find to be an interesting property of how these models calculate the probability that data D were generated by a particular causal graph G. To do so we will present a modified version of the notation presented in Carroll et al. (2013). For generative causes, the likelihood of the data D under a particular parameterization of graph G was defined as p(D|w,G) = p(e|c,w,G)!(!,c)