Children posit hidden causes to explain causal variability

Children posit hidden causes to explain causal variability David W. Buchanan (david buchanan@brown.edu) and David M. Sobel (dave sobel@brown.edu) Department of Cognitive, Linguistic, and Psychological Sciences Box 1821, Brown University, Providence, RI, 02912 Abstract Most models of causal reasoning estimate the strength of a causal relation using a function of the proportion of successes and failures: the number of trials on which the cause produced the effect, divided by the total number of trials. Alternatively, people may represent failures as due to a hidden inhibitor that has a specific location and extent in time. We model these pos- sibilities, and empirically test a case on which the two mod- els make opposite predictions. We find that children as young as four years old generate responses inconsistent with propor- tional models, but consistent with an inhibitor-based model. Incorporating a recency component does not help proportional models fit the data. Keywords: causal reasoning, cognitive development, models of causal reasoning, hidden Markov models. Introduction Causal relations do not always hold. For instance, turning your key starts your car, but most of us have had an experi- ence with a car that did not start when we turned the key in the ignition. Some of us own reliable cars, where this hap- pens infrequently, whereas others of us own cars where this happens often. How do people represent such differences in variability? One approach is to see variable causal relations as essen- tially probabilistic: causal relations sometimes randomly fail. In this case, it is natural to estimate the strength of the re- lation using some function of the proportion of successes to total trials. For instance, if your car started 6 days out of 10 in the past, you might estimate that the probability of it starting the next day, was 0.6. Most models from the causal reasoning literature either directly use, or converge to, such a propor- tion or a function of such a proportion. These include most associative (e.g., Rescorla & Wagner, 1972), causal power (e.g., Cheng, 1997) and neural network (e.g., McClelland & Thompson, 2007) models of causal reasoning. Not all of these models are deeply committed to using simple propor- tions, but most currently do. We will refer to such models as proportional models. There is an alternative to the proportional approach: it could be that variability is the result not of intrinsic random- ness, but rather the result of changing hidden inhibitors that tend to persist in time. For instance, it is possible that cold weather prevented the engine from turning over, or your bat- tery needed to be replaced, or some other unknown problem existed. Under such an inhibitor-based model, judging the probability of success involves judging whether the causes responsible for past failures, might be active on the next trial. For instance, if your car usually starts six days out of ten, then you can reason that whatever hidden causes are responsible for the four failures out of ten, are 40 percent likely to occur tomorrow. As this example illustrates, there are many cases in which proportional and inhibitor-based approaches make the same predictions. Given that inhibitor-based approaches in- troduce new complexity, it is understandable that researchers have focused on proportional models. There are, however, some cases in which the two classes of models make different predictions. One of these cases oc- curs when we must reason about a novel intervention. For in- stance, imagine you own a new car that has never had a prob- lem starting. On Monday, your friend, an amateur mechanic, opens the hood and makes some “improvements.” On Tues- day, your car fails to start. Without further repairs, it seems unlikely your car would start on Wednesday. On the other hand, imagine if the car was old junker, that normally only started half the time – it had failed on Thursday and Saturday, but started on Friday and Sunday. As above, your mechanic friend fiddles under the hood on Monday, and on Tuesday it fails to start. In this case, it seems less likely that the car will fail again on Wednesday. The fact that the car sometimes failed before, then recovered, makes you more confident that it will recover again. Some experimental data suggests that children represent hidden inhibitors, when shown a novel, variable causal re- lation. Schulz and Sommerville (2006) showed 4.5 year-old children a machine that lit up and played music when a but- ton was pressed. They also showed children a ring that when placed on the machine, appeared to prevent the machine from working. In the probabilistic condition, children then saw a period in which the machine activated on only a few trials, in the following pattern: [0 1 0 0 0 0 1 0] 1 In the deterministic condition, children saw eight successes: [1 1 1 1 1 1 1 1]. At test, children in both conditions were presented with a choice: they could disable the machine using the ring (which they had seen work as a disabler before), or they could disable the machine using a candidate cause (a small flashlight) that had been hidden during the rest of the procedure. Children were significantly more likely to choose the flashlight in the prob- abilistic than in the deterministic condition. This result sug- gests that the probabilistic activation implied, to the children, the existence of a hidden inhibitor. A proportional model can- not explain this effect, since the calculation of causal strength in both conditions should be qualitatively the same. Schulz and Sommerville (2006)’s data provide support for a model that explicitly incorporates hidden inhibitors. To our knowledge, no experiment exists that directly compares the predictions of inhibitor-based, and proportional approaches. 1 This notation means: one failure, one success, then four fail- ures, followed by one success, followed by one failure. This notation will be used throughout the paper.