At each stage of a bayesian dialogue, each of two interlocutors states his beliefs formed after the revision prompted by the beliefs stated by the other at the previous stage. A third party, with access only to the transcript of a dialogue, cannot distinguish a bayesian dialogue from an arbitrary sequence of pairs of utterances. Equivalently, two rational individuals who learn from each other can hold different, even divergent beliefs for any number of rounds of communication.

The knowledge and belief of two individuals is modelled by two partitions of a probability space. Starting with an individual's partition, a learning process for the individual is a sequence of partitions, each a refinement of its predecessor. The probabilities ascribed by an individual along the process to a fixed event form a sequence of numbers called a monologue concerning this event. A dialogue is a pair of two monologues, one for each individual, concerning the same event such that the refinements are achieved by publicly announcing the probabilities in each stage. We introduce a new measure of fluctuation of sequences that we call relative variation and characterize the sequences of probabilities that are monologues in terms of this measure. We provide a necessary and sufficient condition for two sequences of probabilities to make a dialogue, in terms of their joint fluctuation, showing that two monologues do not necessarily make a dialogue.


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