Superseding Venn information diagrams with partial entropy decomposition

Decomposing a joint entropy dates back to at least 1961, when it was shown that entropy operations addition and subtraction were isomorphic to the union and intersection operations of sets. This gave rise to displaying entropy on Venn diagrams. However, these Venn diagrams suffer from the well-known problem that regions where more than two terms intersect could have "negative information." I present a novel decomposition of joint entropy into a sum of non-negative regions where each region has a natural interpretation as the entropy common among those terms.