Quantitative causal selection patterns in token causation

When many events contributed to an outcome, people consistently judge some more causal than others, based in part on the prior probabilities of those events. For instance, when a tree bursts into flames, people judge the lightning strike more of a cause than the presence of oxygen in the air -- in part because oxygen is so common, and lightning strikes are so rare. These effects, which play a major role in several prominent theories of token causation, have largely been studied through qualitative manipulations of the prior probabilities. Yet, there is good reason to think that people's causal judgments are on a continuum -- and relatively little is known about how these judgments vary quantitatively as the prior probabilities change. In this paper, we measure people's causal judgment across parametric manipulations of the prior probabilities of antecedent events. Our experiments replicate previous qualitative findings, and also reveal several novel patterns that are not well-described by existing theories.