  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
$\phi$.
