I like this paper in Entropy. I keep going back to it. I think because it gives me permission to allow for macro causation to effect the micro; the constraints upon the micro which allow the micro to happen; in this case, by analogizing to Claude Shannon’s channel capacity – and it works.
“The theory of causal emergence directly challenges the reductionist assumption that the most informative causal model of any system is its microscale. Causal emergence reveals a contrasting and counterintuitive phenomenon: sometimes the map is better than the territory. As shown here, this has a precedent with Shannon’s discovery of the capacity of a communication channel, which was also thought of as counterintuitive at the time. Here an analogous idea of a causal capacity of a system has been developed using effective information. Effective information, an information-theoretic measure of causation, is assessed by the application of an intervention distribution. However, in the construction of causal models, particularly those representing higher scales, model choice warps the intervention distribution. This can lead to a greater usage of the system’s innate causal capacity than its microscale representation. In general, causal capacity can approach the channel capacity, particularly as degrees of model choice increase. The choice of a model’s scale, its elements and states, its background conditions, its initial conditions, what variables to leave exogenous and in what manner, and so on, all result in warping of the intervention distribution ID. All of these make the state-space of the system smaller, so can be classified as macroscales, yet all may possibly lead to causal emergence.”