The literature on attitudes toward objects includes seminal research on threat appraisals indicating that individuals locate an object in a multidimensional threat appraisal space defined by the object's perceived degree of being good or bad, weak or strong, and passive or active. We advance this research in three ways. First, we generalize the information integration on an object with the inclusion of other individuals’ displayed appraisals, and posit the existence of a dynamical system of information integration that generates a network of interpersonal influences on group members’ object appraisals. Second, we show that this influence system entails a set of non-obvious and rarely violated constraints on individuals’ settled appraisals. Third, with data collected in experiments on groups’ appraisals of images of nine animals and two nations, Russia and North Korea, we report empirical findings that support the existence of this system and its predicted constraints on individuals’ object appraisals.