There exist low-dimensional models of holography in which the bulk gravitational theory is dual to an ensemble average of boundary quantum field theories (as opposed to a single theory). In the case of three-dimensional gravitational theories based on topological field theories, we draw a connection between the ensemble averaging (and the lack of factorization of the partition function) and the presence of global symmetries. Once the global symmetries are removed (by a suitable gauging procedure), the gravitational theory behaves as a unitary quantum system.; Part of London TQFT Journal Club; please register at https://www.london-tqft.co.uk;