A familiar dilemma for the subset theory of realization

I argue that the subset theory of property realization cannot account for both the multiple realizability and causal efficacy of mental properties. It avoids the threat of causal exclusion by identifying every power of a realized property with some power of its realizer, but this entails that the different realizers of a multiply realizable property share their causal powers, and this just isn't so. A counterexample is produced as evidence. Thus, in its original form, the theory fails to account for the multiple realizability of mental properties. The theory can be amended to account for multiple realizability, but these amendments undermine its account of mental causation and thereby reintroduce the problem of causal exclusion. The subset theory is thus caught between the horns of a familiar dilemma for physicalist theories of mind.