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). This study presents an Agent Based Model (ABM) based on Conceptual Agreement Theory (CAT), which models social agreement as a simplified communicational event in which an Observer (O) and Actor (A) exchange ideas about a concept C, and where O uses that information to infer whether A's conceptual state is the same as its own (i.e., to infer agreement). Agreement may be true (when O infers that A is thinking C and this is in fact the case, event a1) or illusory (when O infers that A is thinking C and this is not the case, event a2). In CAT, concepts that afford a1 or a2 become more salient in the minds of members of social groups. Results from the ABM 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. 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.