Intersection democracy for winding branes and stabilization of extra dimensions

We show that, in the context of pure Einstein gravity, a democratic principle for intersection possibilities of branes winding around extra dimensions in a given partitioning yield stabilization, while what the observed space follows is matter-like dust evolution. Here democracy is used in the sense that, in a given decimation of extra dimensions, all possible wrappings and hence all possible intersections are allowed. Generally, the necessary and sufficient condition for this is that the dimensionality m of the observed space dimensions obey 3⩽m⩽N for N⩾3, where N is the decimation order of the extra dimensions.