Abstract. I will explore the idea that certain theories of gravity in Anti-de Sitter space are dual to an average over an ensemble of quantum theories, rather than to a specific quantum theory. I will describe an average over Narain’s family of two-dimensional conformal field theories which describe free bosons on a torus, and compute the partition function using the Siegel-Weil formula. The result takes the form of a sum over geometries as one would expect in a theory of gravity. But the gravitational theory looks more like a Chern-Simons theory than like Einstein gravity.