Abstract We review a recently introduced model in which each of a number of agents is endowed with an abstract argumentation framework reflecting her individual views regarding a given set of arguments. A question arising in this context is whether the diversity of views observed in such a situation is consistent with the assumption that every individual argumentation framework is induced by a combination of, first, some basic factual information and, second, the personal preferences of the agent concerned. We treat this question of rationalisability of a profile as an algorithmic problem and identify tractable and intractable cases. This is useful for understanding what types of profiles can reasonably be expected to occur in a multiagent system