  Collective phenomena in systems of interacting agents have helped us
understand diverse social, ecological and biological observations. The
corresponding explanations are challenged by incorrect information processing.
In particular, the models typically assume a shared understanding of signals or
a common truth or value system, i.e., an agreement of whether the measurement
or perception of information is `right' or `wrong'. It is an open question
whether a collective consensus can emerge without these conditions. Here we
introduce a model of interacting agents that strive for consensus, however,
each with only a subjective perception of the world. Our communication model
does not presuppose a definition of right or wrong and the actors can hence not
distinguish between correct and incorrect observations. Depending on a single
parameter that governs how responsive the agents are to changing their
world-view we observe a transition between an unordered phase of individuals
that are not able to communicate with each other and a phase of an emerging
shared signalling framework. We find that there are two types of
convention-aligned clusters: one, where all social actors in the cluster have
the same set of conventions, and one, where neighbouring actors have different
but compatible conventions (`stable misunderstandings').
