Intersection Information Based on Common Randomness

Since the seminal paper [1], there's been a flurry of research [2-5] towards defining an intersection information that quantifies how much of “the same information” two or more random variables specify about a target random variable. 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 which is the first to satisfy the coveted Target Monotonicity property. Our measure is imperfect and we suggest directions for improvement.