Additive multi-attribute value models and additive utility models with discrete outcome sets are widely applied in both descriptive and normative decision analysis. Their non-parametric application allows preference inference by analyzing sets of general additive value functions compatible with the observed or elicited holistic pair-wise preference statements. In this paper, we provide necessary and sufficient conditions for the preference inference based on a single preference statement, and sufficient conditions for the inference based on multiple preference statements. In our computational experiments all inferences could be made with these conditions. Moreover, our analysis suggests that the non-parametric analyses of general additive value models are unlikely to be useful by themselves for decision support in contexts where the decision maker preferences are elicited in the form of holistic pair-wise statements.