  It is argued that the observed vacuum energy density and the small values of
the neutrino masses could be due to anthropic selection effects. Until now,
these two quantities have been treated separately from each other and, in
particular, anthropic predictions for the vacuum energy were made under the
assumption of zero neutrino masses. Here we consider two cases. In the first,
we calculate predictions for the vacuum energy for a fixed (generally non-zero)
value of the neutrino mass. In the second we allow both quantities to vary from
one part of the universe to another. We find that the anthropic predictions for
the vacuum energy density are in a better agreement with observations when one
allows for non-zero neutrino masses. We also find that the individual
distributions for the vacuum energy and the neutrino masses are reasonably
robust and do not change drastically when one adds the other variable.
