Preventative Scope in Causation

Preventative Scope in Causation Christopher D. Carroll (cdcarroll@ucla.edu) Department of Psychology, UCLA Patricia W. Cheng (cheng@lifesci.ucla.edu) Department of Psychology, UCLA Abstract generative cause and a broad preventer whose preventative scope includes all of the generative causes of the effect. Preventative scope can be inferred by observing the frequency of the effect as a function of its causes and the preventer. Even in the simplest situation where only one generative cause is known, a broad preventer and a narrow preventer predict different patterns of covariation between the generative cause, the preventer, and the effect. To see why, consider the influence of the preventer when the generative cause is absent. When an effect occurs in the absence of a known cause, its occurrence is often attributed to one or more unknown or unobserved causes (Hagmayer & Waldmann, 2007; Luhmann & Ahn, 2007; Saxe, Tenenbaum, & Carey, 2005). By definition, a broad preventer stops these unknown causes from producing the effect, and a narrow preventer does not. Broad prevention should influence the frequency of the effect even when the generative cause is absent, whereas narrow prevention should not do so. More formally, for causes and effects that are binary (either present or absent), it is possible to derive the probability of the effect as a function of the generative cause, the preventer, and the preventative scope of the preventer. We do so by adopting the assumptions in Cheng (1997) and adding the assumption of preventative scope. Letting p c be the causal power of the generative cause, p p be the causal power of the preventer, and p a be the causal power of the causal background (representing causal power and frequency of the unknown causes of the effect in the current context), we obtain the equations for broad prevention and narrow prevention that are shown in Table 1. Some preventers only stop an effect when it is being produced by certain causes. For example, nasal spray prevents headaches caused by a cold but not headaches caused by dehydration or stress. Thus, preventers differ in preventative scope: the range of circumstances across which a preventer operates. An experiment indicated that people are sensitive to differences in preventative scope and that participants are more likely to generalize prevention when the preventer has a broad preventative scope. Additional evidence suggested that people take preventative scope into account when attempting to explain how prevention operates. Keywords: causality; causal power; prevention; hidden causes Preventative Scope What does it mean for one thing to prevent another? While many models of causal reasoning include prevention (e.g., Cheng, 1997; Griffiths & Tenenbaum, 2005), few studies have examined how well prevention in these models corresponds to everyday notions of prevention. One aspect of prevention that is found in everyday reasoning but poorly represented in formal models is preventative scope: the range of circumstances across which the preventer works. We define preventative scope relative to the causes of the effect. A preventer with a broad preventative scope stops the effect no matter what the cause. A preventer with a narrow preventative scope stops the effect only when certain causes are responsible for producing the effect. The difference between broad prevention and narrow prevention can be illustrated by contrasting the influences of aspirin and nasal spray on headaches. Aspirin prevents headaches caused by colds, headaches caused by dehydration, and headaches caused by stress. Nasal spray prevents headaches caused by colds, but not headaches caused by dehydration or stress. Thus, aspirin has a broad preventative scope and nasal spray has a narrow preventative scope. An experiment was conducted to investigate preventative scope. The goals of the experiment were to determine (1) whether people are sensitive to preventative scope, (2) how preventative scope is generalized to situations where there is a novel generative cause, and (3) how people interpret or explain preventative scope. Table 1: Probability of effect as a function of cause c and preventer p broad prevention Broad and narrow prevention In the current investigation, we restrict ourselves to the extremes of preventative scope: we contrast a narrow preventer whose preventative scope includes only a single narrow prevention P(e|~c,~p) p a p a P(e|c,~p) p a  p c − p a p c p a  p c − p a p c P(e|~c,p) p a 1− p p  p a P(e|c,p) p a 1− p p   p c 1− p p  − p a p c 1− p p  p a  p c 1− p p  − p a p c 1− p p 