  Krause's model of opinion dynamics has recently been the object of several
studies, partly because it is one of the simplest multi-agent systems involving
position-dependent changing topologies. In this model, agents have an opinion
represented by a real number and they update it by averaging those agent
opinions distant from their opinion by less than a certain interaction radius.
Some results obtained on this model rely on the fact that the opinion orders
remain unchanged under iteration, a property that is consistent with the
intuition in models with simultaneous updating on a fully connected
communication topology. Several variations of this model have been proposed. We
show that some natural variations are not order preserving and therefore cause
potential problems with the theoretical analysis and the consistence with the
intuition. We consider a generic version of Krause's model parameterized by an
influence function that encapsulates most of the variations proposed in the
literature. We then derive a necessary and sufficient condition on this
function for the opinion order to be preserved.
