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 $3leqm le N$ where $N$ is the decimation order of the extra dimensions.