Quantifying causal emergence shows that macro can beat micro

Properly characterizing emergence requires a causal approach. Here, we construct causal models of simple systems at micro and macro spatiotemporal scales and measure their causal effectiveness using a general measure of causation [effective information (EI)]. EI is dependent on the size of the system's state space and reflects key properties of causation (selectivity, determinism, and degeneracy). Although in the example systems the macro mechanisms are completely specified by their underlying micro mechanisms, EI can nevertheless peak at a macro spatiotemporal scale. This approach leads to a straightforward way of quantifying causal emergence as the supersedence of a macro causal model over a micro one.