The paper deals with application of several emerging approaches to mass appraisal (valuations). The empirical part uses a sample of more than 100 residential properties in a neighbourhood of Amsterdam to compare the valuation accuracy of three methods: multiple regression analysis, the self-organizing map (a neural network method) and rough set theory (a method related to fuzzy logic) for mass appraisal. Our aim is pragmatical: we anchor our approach on recent (relevant) literature on methodological comparisons and innovations, and continue by reporting value modelling work that we have carried out ourselves. The main criterion is accuracy of valuations in relation to actual observations, using a test sample. Additional criteria, such as feasibility and conceptual soundness, are proposed too. Our further aim is to strongly encourage follow up from our peers. Therefore, our work is also an opportunity to develop a protocol for critical evaluation of new mass appraisal methodologies. The results shows that an alternative approach may reach results close to those from regression analysis. Furthermore, the unorthodox methods may fit better in those markets where formal (orthodox) mathematical modelling is inefficient due to the inability to capture latent factors (i.e. effects that we do not know of or cannot record) and/or to unrealistic arbitrage assumptions for example due to asymmetric information. Such markets are characterised by non-linearities and multiple equilibria.