From micro to macro units: a mathematical framework for identifying the causal grain of a system from its intrinsic perspective

Abstract Integrated information theory (IIT) aims to account for the quality and quantity of consciousness in physical terms. According to IIT, a substrate of consciousness must be a system of units that is a maximum of intrinsic, irreducible cause-effect power, quantified by integrated information ( φ s ). Moreover, the grain of each unit must be the one— from micro (finer) to macro (coarser)—that maximizes the system’s intrinsic irreducibility (i.e., maximizes φ s ). The units that maximize φ s are called the intrinsic units of the system. This work extends the mathematical framework of IIT 4.0 to assess cause-effect power at different grains and thereby determine a system’s intrinsic units. Using simple, simulated systems, we show that the cause-effect power of a system of macro units can be higher than the cause-effect power of the corresponding micro units. Two examples highlight specific kinds of macro units, and how each kind can increase cause-effect power. The implications of the framework are discussed in the broader context of IIT, including how it provides a foundation for tests and inferences about consciousness.