What is the best way of discovering the underlying structure of a causal system composed of multiple variables? One prominent idea is that learners should manipulate each candidate variable in isolation to avoid confounds (sometimes known as the "Control of Variables" or CV strategy). We demonstrate that CV is not always the most efficient method for learning. Using an optimal actor model which aims to minimize the average number of tests, we show that when a causal system is sparse (i.e., when the outcome of interest has few or even just one actual cause among the candidate variables) it is more efficient to test multiple variables at once. Across a series of behavioral experiments, we then show that people are sensitive to causal sparsity and adapt their strategies accordingly. When interacting with a non-sparse causal system (high proportion of actual causes among candidate variables), they use a CV strategy, changing one variable at a time. When interacting with a sparse causal system they are more likely to test multiple variables at once. However, we also find that people sometimes use a CV strategy even when a system is sparse.
IntroductionTo develop a causal understanding of the world, we often need to find out how multiple candidate variables affect an outcome of interest. This problem arises in everyday situations (e.g., "Which switch(es) control the bathroom fan?"), during scientific exploration ("Which of these treatments can affect disease x?"), and plays an important part in answering economic and social questions ("What is the impact of these policies on Gross Domestic Product?"). Often, the quickest and most effective method of resolving causal relationships is to conduct experiments that manipulate variables of a system (e.g., turning switches on or off) and to observe the resulting outcome. This kind of causal experimentation is often (but not always) required to decouple causation and correlation (Pearl, 2009;Woodward, 2005;Sloman, 2005).Both children and adults can systematically leverage the outcomes of interventions to test causal hypotheses that would be indistinguishable based on observation alone (Lagnado & Sloman, 2004; Lagnado, Waldmann, Hagmayer, & Sloman, 2006;Rottman & Keil, 2012;Schulz, Gopnik, & Glymour, 2007;Sloman & Lagnado, 2005;Waldmann & Hagmayer, 2005). Furthermore, people are sometimes able to come up with highly efficient experiments that optimize information gained per intervention or minimize the total number of tests needed on average to discover the true causal structure (Bramley, Lagnado, & Speekenbrink, 2015;Bramley, Dayan, Griffiths, & Lagnado, 2017; Coenen, Rehder, & Gureckis, 2015;Steyvers, Tenenbaum, Wagenmakers, & Blum, 2003).Here we consider a specific learning situation in which people are asked to explore a causal system consisting of a number of independent variables (switches) and a dependent outcome (turning on a fan). These types of problems have played a central role in research on science education and cognitive development and are common in ...