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Collective phenomena in systems of interacting agents have helped usunderstand diverse social, ecological and biological observations. Thecorresponding explanations are challenged by incorrect information processing.In particular, the models typically assume a shared understanding of signals ora common truth or value system, i.e., an agreement of whether the measurementor perception of information is `right' or `wrong'. It is an open questionwhether a collective consensus can emerge without these conditions. Here weintroduce a model of interacting agents that strive for consensus, however,each with only a subjective perception of the world. Our communication modeldoes not presuppose a definition of right or wrong and the actors can hence notdistinguish between correct and incorrect observations. Depending on a singleparameter that governs how responsive the agents are to changing theirworld-view we observe a transition between an unordered phase of individualsthat are not able to communicate with each other and a phase of an emergingshared signalling framework. We find that there are two types ofconvention-aligned clusters: one, where all social actors in the cluster havethe same set of conventions, and one, where neighbouring actors have differentbut compatible conventions (`stable misunderstandings').

Collective patterns and stable misunderstandings in networks striving for consensus without a common value system