The initial state parameters s0 and w0 are intricate issues of the averaging cognitive models in Information Integration Theory. Usually they are defined as a measure of prior information (Anderson, 1981; 1982) but there are no general rules to deal with them. In fact, there is no agreement as to their treatment except in specific situations such as linear models where they can be merged with the arbitrary zero inter-response scale C0. We present some considerations on their meaning and usefulness in the Functional Measurement approach, starting from different points of view. Furthermore, we suggest a method to deal with their complexity both within each single trial of a factorial design, and between the overall trials of an experiment.