  Current cosmological observations indicate a preference for a cosmological
constant that is drastically smaller than what can be explained by conventional
particle physics. The Causal Entropic Principle (Bousso, {\it et al}.) provides
an alternative approach to anthropic attempts to predict our observed value of
the cosmological constant by calculating the entropy created within a causal
diamond. We have extended this work to use the Causal Entropic Principle to
predict the preferred curvature within the "multiverse". We have found that
values larger than $\rho_k = 40\rho_m$ are disfavored by more than 99.99% and a
peak value at $\rho_{\Lambda} = 7.9 \times 10^{-123}$ and $\rho_k =4.3 \rho_m$
for open universes. For universes that allow only positive curvature or both
positive and negative curvature, we find a correlation between curvature and
dark energy that leads to an extended region of preferred values. Our universe
is found to be disfavored to an extent depending the priors on curvature. We
also provide a comparison to previous anthropic constraints on open universes
and discuss future directions for this work.
