Many governments wish to assess the quality of their universities. A prominent example is the UK’s new Research Excellence Framework (REF) 2014. In the REF, peer-review panels will be provided with information on publications and citations. This paper suggests a way in which panels could choose the weights to attach to these two indicators. The analysis draws in an intuitive way on the concept of Bayesian updating (where citations gradually reveal information about the initially imperfectly-observed importance of the research). Our study should not be interpreted as the argument that only mechanistic measures ought to be used in a REF.