  Probabilistic argumentation allows reasoning about argumentation problems in
a way that is well-founded by probability theory. However, in practice, this
approach can be severely limited by the fact that probabilities are defined by
adding an exponential number of terms. We show that this exponential blowup can
be avoided in an interesting fragment of epistemic probabilistic argumentation
and that some computational problems that have been considered intractable can
be solved in polynomial time. We give efficient convex programming formulations
for these problems and explore how far our fragment can be extended without
loosing tractability.
