  We define an index of compatibility for a probabilistic theory (PT). Quantum
mechanics with index 0 and classical probability theory with index 1 are at the
two extremes. In this way, quantum mechanics is at least as incompatible as any
PT. We consider a PT called a concrete quantum logic that may have
compatibility index strictly between 0 and 1, but we have not been able to show
this yet. Finally, we show that observables in a PT can be represented by
positive, vector-valued measures.
