Many social phenomena can be viewed as processes in which individuals in social groups develop agreement (e.g., public opinion, the spreading of rumor, the formation of social and linguistic conventions). Conceptual Agreement Theory (CAT) models social agreement as a simplified communicational event in which an Observer and Actor exchange ideas about a concept , and where uses that information to infer whether 's conceptual state is the same as its own (i.e., to infer agreement). Agreement may be true (when infers that is thinking and this is in fact the case, event ) or illusory (when infers that is thinking and this is not the case, event ). In CAT, concepts that afford or become more salient in the minds of members of social groups. Results from an agent-based model (ABM) and probabilistic model that implement CAT show that, as our conceptual analyses suggested would be the case, the simulated social system selects concepts according to their usefulness to agents in promoting agreement among them (Experiment 1). Furthermore, the ABM exhibits more complex dynamics where similar minded agents cluster and are able to retain useful concepts even when a different group of agents discards them (Experiment 2). We discuss the relevance of CAT and the current findings for analyzing different social communication events, and suggest ways in which CAT could be put to empirical test.