I think we are talking about independent samples of X and Y, not about time series. If X causes Y, then you model y = f(x, u), where U is a random variable independent of X (think: unexplained, e.g. noise). I don't think there can be any dampening effect in this setup. This model is generic: you can find a f(x, u) for any relationship between X and Y. But you may get a much simpler noise model (like additive gaussian noise) in one direction. It's no proof, but a strong hint (Occam's razor). There is also the family of algorithms like IC* and FCI that can recover a causal graph from statistical dependencies between random variables. As output you get a set of causal graphs that are still plausible given the observed dependencies, including constraints about the presence or absence of latent common causes.