Compactifying de Sitter Naturally Selects a Small Cosmological Constant

We study compactifications of $D$-dimensional de Sitter space with a $q$-form flux down to $D-Nq$ dimensions. We show that for $(N-1)(q-1)\geq 2$ there are double-exponentially or even infinitely many compact de Sitter vacua, and that their effective cosmological constants accumulate at zero. This population explosion of $\Lambda \ll 1$ de Sitters arises by a mechanism analogous to natural selection.