A Principled Infotheoretic \phi-like Measure

Integrated information theory is a mathematical, quantifiable theory of conscious experience. The linchpin of this theory, the $\phi$ measure, quantifies a system's irreducibility to disjoint parts. Purely as a measure of irreducibility, we pinpoint three concerns about $\phi$ and propose a revised measure, $\psi$, which addresses them. Our measure $\psi$ is rigorously grounded in Partial Information Decomposition and is faster to compute than $\phi$.