The study of consumer psychology reveals two categories of consumption decision procedures: compensatory rules and non-compensatory rules. Existing recommendation models which are based on latent factor models assume the consumers follow the compensatory rules, i.e. they evaluate an item over multiple aspects and compute a weighted or/and summated score which is used to derive the rating or ranking of the item. However, it has been shown in the literature of consumer behavior that, consumers adopt non-compensatory rules more often than compensatory rules. Our main contribution in this paper is to study the unexplored area of utilizing non-compensatory rules in recommendation models.Our general assumptions are (1) there are K universal hidden aspects. In each evaluation session, only one aspect is chosen as the prominent aspect according to user preference. (2) Evaluations over prominent and non-prominent aspects are non-compensatory. Evaluation is mainly based on item performance on the prominent aspect. For non-prominent aspects the user sets a minimal acceptable threshold. We give a conceptual model for these general assumptions. We show how this conceptual model can be realized in both pointwise rating prediction models and pair-wise ranking prediction models. Experiments on real-world data sets validate that adopting non-compensatory rules improves recommendation performance for both rating and ranking models.