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

Integrated information theory (IIT) aims to account for the quality and quantity of consciousness in physical terms. It starts from the essential properties of experience, the theory's axioms, which it translates into postulates of cause-effect power - the ability of the system's units to take and make a difference. Based on the theory's postulates, a substrate of consciousness must be a system of units that is a maximum of intrinsic, irreducible cause-effect power. Moreover, the grain of the substrate's units must be the one that ensures maximal intrinsic irreducibility. This work employs the mathematical framework of IIT 4.0 to assess cause-effect power at different unit grains according to the theory's postulates. 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. ### Competing Interest Statement G.T. holds an executive position and has a financial interest in Intrinsic Powers, Inc., a company whose purpose is to develop a device that can be used in the clinic to assess the presence and absence of consciousness in patients. This does not pose any conflict of interest with regard to the work undertaken for this publication.