It is often argued that if a mentalproperty supervenes on a physical property, then (1)the mental property M ``inherits'' its causal efficacyfrom the physical property P and (2) the causalefficacy of M reduces to that of P. However, once weunderstand the supervenience thesis and the concept ofcausation probabilistically, it turns out that we caninfer the causal efficacy of M from that of P andvice versa if and only if a certain condition, whichI call the ``line-up'' thesis, holds. I argue that thesupervenience thesis entails neither this conditionnor its denial. I also argue that even when theline-up thesis holds true, reductionism about thecausal efficacy of the mental property doesn'tfollow.