This article develops axiomatic foundations for a probabilistic theory of causal strength as difference-making. I proceed in three steps: First, I motivate the choice of causal Bayes nets as an adequate framework for defining and comparing measures of causal strength. Second, I prove several representation theorems for probabilistic measures of causal strength—that is, I demonstrate how these measures can be derived from a set of plausible adequacy conditions. Third, I use these results to argue for a specific measure of causal strength: the difference that interventions on the cause make for the probability of the effect. I conclude by discussing my results and outlining future research avenues.
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