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Seeing the Unobservable – Inferring the Probability and Impact of Hidden Causes

Seeing the Unobservable – Inferring the Probability and Impact of Hidden Causes York Hagmayer (york.hagmayer@bio.uni-goettingen.de) Department of Psychology, University of Gottingen, Gosslerstr. 14 37073 Gottingen, Germany Michael R. Waldmann (michael.waldmann@bio.uni-goettingen.de) Department of Psychology, University of Gottingen, Gosslerstr. 14 37073 Gottingen, Germany Abstract Theoretical Accounts of Hidden Causes The causal impact of an observable cause can only be esti- mated if assumptions are made about the presence and impact of possible additional unobservable causes. Current theories of causal reasoning make different assumptions about hidden causes. Some views assume that hidden causes are always present, others that they are independent of the observed causes. In two experiments we assessed people’s assumptions about the occurrence and statistical relations involving a hid- den cause. In the experiments, participants either only ob- served a cause or actively manipulated it. We assessed par- ticipants’ assumption online after each learning trial and at the end of the learning phase. The results show an interesting dissociation. Whereas there was a tendency to assume nega- tive correlation in the online judgments, the final judgments tended more in the direction of an independence assumption. It could also be shown that the judgments were generally co- herent with the learning data. These results are consistent with normative theories that drop independence as the default assumption. We are going to focus on a simple causal structure consist- ing of a single observable cause C and one possible hidden cause A both influencing a joint observable effect E. The two observable events C and E are statistically related. Cause C is neither sufficient nor necessary for the effect, P(e|c) 0. How can the causal impact of the observed and - if possible - the impact of the hidden cause be assessed in such a situation? Associative Theories and the Constant-Background Assumption Introduction Most events are causally influenced by more than a single cause. Unfortunately, very often these other causes are un- known or cannot be easily observed. Therefore we often have to rely on the observed statistical relationship between cause and effect when assessing causal strength. For exam- ple, whenever a new influenza virus invades East Asia, health representatives try to estimate its health risks, well aware of the fact that many other factors determine whether a patient will die or not. The question of how to assess causal strength when there are hidden causes has challenged normative theories of causality and psychological theories of causal reasoning for some time. A number of different ac- counts have been proposed analyzing how the causal impact of an observed factor can be accurately estimated if certain assumptions are made about potential hidden causes. In this report we will first give a brief overview of how two current theories of causal reasoning handle hidden causes. In the second part of the report we will present two experiments in which we assessed the assumptions of learners about the impact and probability of hidden causes. In the final section we will discuss potential theoretical implications of these findings. Associative theories, such as the Rescorla-Wagner theory (Rescorla & Wagner, 1972), would model this task as learn- ing about the association between a cue representing the observed cause and an outcome representing the effect. Along with the cause cue a second background (or context) cue would be part of the model. This background cue is as- sumed to be always present and to represent all other factors that might also generate the outcome. Thus, the background cue would play the role of representing the hidden cause A in the outlined causal model. According to the Rescorla- Wagner rule, only weights of cues that are present in a cer- tain trial are being updated. Therefore the permanently pre- sent background cue will generally compete with the cause cue in cases in which the cause cue is present. If the out- come is also present the associative weights of both cues will be raised, if the outcome is absent, the weights will be lowered. However, in cases in which the cause cue is absent, only the weight of the background cue will be altered. At the asymptote of learning the associative weight of the observed cause will equal the contingency (i.e., ∆P=P(e|c)–P(e|~c)) of the cause cue and the outcome. The associative weight of the background cue will correspond to the probability of the outcome in the absence of the cause cue. Thus, the more often the outcome (=effect) occurs on its own, the higher the associative weight of the background cue will be.