  Motivated by recent work of Bousso and Polchinski (BP), we study theories
which explain the small value of the cosmological constant using the anthropic
principle. We argue that simultaneous solution of the gauge hierarchy problem
is a strong constraint on any such theory. We exhibit three classes of models
which satisfy these constraints. The first is a version of the BP model with
precisely two large dimensions. The second involves 6-branes and antibranes
wrapped on supersymmetric 3-cycles of Calabi-Yau manifolds, and the third is a
version of the irrational axion model. All of them have possible problems in
explaining the size of microwave background fluctuations. We also find that
most models of this type predict that all constants in the low energy
Lagrangian, as well as the gauge groups and representation content, are chosen
from an ensemble and cannot be uniquely determined from the fundamental theory.
In our opinion, this significantly reduces the appeal of this kind of solution
of the cosmological constant problem. On the other hand, we argue that the
vacuum selection problem of string theory might plausibly have an anthropic,
cosmological solution.
