A stochastic model for paired comparisons of multi-attribute social stimuli is proposed where one objective is to find the relative importance of the attributes for a judge. Is is related to the Bradley-Terry model where log-parameters are linear combinations of functions of the stimuli's attributes. This model neither assumes that the functions are fixed given in advance nor that different judges have the same set of functions. The choice among such functions, however, is admitted only within a finite given scope. Within the framework of exponential families maximum likelihood estimators and tests are derived and applied to data coming from a psychological experiment with schematic faces. Each pair of the 18 schematic faces was presented to 36 judges in groups of four by projecting the 2 corresponding slides onto a screen in random order. The judges decided spontaneously which one of the two faces looked more likeable by crossing one of two boxes. In this manner, 153 decisions were recorded for each judge. (Author/RL)