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one of the most robust findings from experimental philosophy is that causal judgments are influenced by relevant norms: people think the SUV running a red light caused the accident and the firefighter who worked on an off-day stopped the fire, even when other candidate causes were present

researchers have now found similar effects for different causal structures (e.g., double prevention) and kinds of norms (e.g., prescriptive norms), as well as other kinds of judgments (e.g., intentionality). this has led to the notion that norms have a general and pervasive effect on modal cognition

but all of this work focuses on judgments of *binary* causes: events that either happen or don't. what happens when candidate causes can contribute in degrees? to find out, we adapted a well-studied binary causal structure (b) so that (c) E happens if C+A > theta (where theta is some threshold)

next, we had participants learn the structure (within a cover story) and the distributions of C and A over 40 trials. the variables were set so that C either had a lower variance (experiment 1) or mean (experiment 2) to A, and manipulation checks confirmed that participants learned this

we then presented participants with a final case where C and A contributed equal amounts to E. after judging the extent to which C caused E, participants rated how surprised they were that C and A took the values they did, confirming that they saw C as violating a statistical norm

nevertheless, participants gave the same causal judgments of C regardless of whether it violated a statistical norm or not! they were also highly confident regardless of normality, indicating that this is not because they were confused about the task

while we don't have a full model, participants' written reports point to a focus on actual contribution over necessity and sufficiency. though some might interpret this as evidence for productive concept of causation, we are optimistic that difference-making theories can stand up to this challenge

most importantly, we think our results help shift the explanatory target from not only *that* norms influence causal judgments, but *when* and *in which contexts* norms matter. they also show that it will take some hard work to generalize our theories of causal judgment to more realistic domains

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