Since the seminal paper Williams and Beers (2010), there's been a flurry of research 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 G\'acs-K\"orner common random variable which is the first to satisfy the coveted Target Monotonicity property. Our measure is imperfect and we suggest directions for improvement.
Intersection Information based on Common Randomness
Virgil Griffith, Edwin K. P. Chong, Ryan G. James, Christopher J. Ellison, James P. Crutchfield