  We first show that the convex effect algebras (CEA) approach to quantum
mechanics is more general than the general probabilistic theories approach. We
then restrict our attention to finite-dimension CEA's. After an introductory
Section~1, we present basic definitions in Section~2. Section~3 studies convex
subeffect algebras and observables. In Section~4 we consider strong CEA's and
strong observables. We show that a CEA is strong if and only if it is
classical. Informationally complete observables on classical CEA's are studied
in Section~5. Section~6 considers quantum CEA's in Hilbert spaces.
