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Krause's model of opinion dynamics has recently been the object of severalstudies, partly because it is one of the simplest multi-agent systems involvingposition-dependent changing topologies. In this model, agents have an opinionrepresented by a real number and they update it by averaging those agentopinions distant from their opinion by less than a certain interaction radius.Some results obtained on this model rely on the fact that the opinion ordersremain unchanged under iteration, a property that is consistent with theintuition in models with simultaneous updating on a fully connectedcommunication topology. Several variations of this model have been proposed. Weshow that some natural variations are not order preserving and therefore causepotential problems with the theoretical analysis and the consistence with theintuition. We consider a generic version of Krause's model parameterized by aninfluence function that encapsulates most of the variations proposed in theliterature. We then derive a necessary and sufficient condition on thisfunction for the opinion order to be preserved.

Order preservation in a generalized version of Krause's opinion dynamics model