Supervenience and causation: A probabilistic approach

It is often argued that if a mental property supervenes on a physical property, then (1) the mental property M "inherits" its causal efficacy from the physical property P and (2) the causal efficacy of M reduces to that of P. However, once we understand the supervenience thesis and the concept of causation probabilistically, it turns out that we can infer the causal efficacy of M from that of P and vice versa if and only if a certain condition, which I call the "line-up" thesis, holds. I argue that the supervenience thesis entails neither this condition nor its denial. I also argue that even when the line-up thesis holds true, reductionism about the causal efficacy of the mental property doesn't follow.