  We consider a wide class of four-dimensional effective field theories in
which gravity is coupled to multiple four-forms and their dual scalar fields,
with membrane sources charged under the corresponding three-form potentials.
Four-form flux, quantised in units of the membrane charges, generically
generates a landscape of vacua with a range of values for the cosmological
constant that is scanned through membrane nucleation. We list various ways in
which the landscape can be made sufficiently dense to be compatible with
observations of the current vacuum without running into the empty universe
problem. Further, we establish the general criteria required to ensure the
absolute stability of the Minkowski vacuum under membrane nucleation and the
longevity of those vacua that are parametrically close by. This selects the
current vacuum on probabilistic grounds and can even be applied in the classic
model of Bousso and Polchinski, albeit with some mild violation of the membrane
weak gravity conjecture. We present other models where the membrane weak
gravity conjecture is not violated but where the same probabilistic methods can
be used to tackle the cosmological constant problem.
