  We show that the maximum quantum violation of the
Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality is exactly the maximum
value satisfying the following principle: The sum of probabilities of pairwise
exclusive events cannot exceed 1. We call this principle "global exclusivity,"
since its power shows up when it is applied to global events resulting from
enlarged scenarios in which the events in the inequality are considered jointly
with other events. We identify scenarios in which this principle singles out
quantum contextuality, and show that a recent proof excluding nonlocal boxes
follows from the maximum violation imposed by this principle to the KCBS
inequality.
