Foundations for a Probabilistic Theory of Causal Strength
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This paper develops axiomatic foundations for a probabilistic theory of causal strength. I proceed in three steps: First, I motivate the choice of causal Bayes nets as a 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 compare these measures on the basis of their characteristic properties, including an application to quantifying causal effect in medicine. Finally, I use the above results to argue for a specific measure of causal strength and I outline future research avenues.