Intersection Information based on Common Randomness

ABSTRACT: The introduction of the partial information decomposition generated a flurry of proposals for defining an intersection information that quantifies how much of &dlquo;the same information^drquo; two or more random variables specify about a target random variable. As yet, none is wholly satisfactory. A palatable measure of intersection information would provide a principled way to quantify slippery concepts such as synergy. Here, we introduce an intersection information measure based on the Gacs-Korner common random variable that is the first to satisfy the coveted Target Monotonicity property. Our measure is imperfect, too, but we suggest directions for improvement.