Abstract: In recent years, a new holographic paradigm has emerged in which simple theories of gravity in low dimensions are dual to statistical ensembles of quantum mechanical systems rather than particular quantum systems. However, more realistic holographic dualities in higher dimensions are not expected to fundamentally involve microscopic averaging. Nevertheless, there are apparently contributions to the semiclassical gravitational path integral that are associated with averaging in the boundary theory. A possibility that reconciles these perspectives is that the apparent averaging is an artifact of coarse-graining over UV degrees of freedom in the low-energy effective theory. In this talk I will define an ensemble of 2D CFT data by averaging over OPE coefficients subject to certain holography-motivated bootstrap constraints, and show that calculations in this ensemble reproduce aspects of semiclassical 3D gravity. I will analyze a variety of gravitational solutions, both in pure Einstein gravity and gravity coupled to massive point particles, including Euclidean wormholes with multiple boundaries and higher topology spacetimes with a single boundary. In all cases we find that the on-shell gravitational action agrees with the ensemble-averaged CFT at large c. I will also show that the bulk effective theory has random couplings induced by wormholes, providing a controlled, semiclassical realization of the Coleman-Giddings-Strominger mechanism.