We present empirical justification of why logistic regression may acceptably approximate, using the number of currently vocalizing interlocutors, the probabilities returned by a time-invariant, conditionally independent model of turn-taking. The resulting parametric model with 3 degrees of freedom is shown to be identical to an infinite-range Ising antiferromagnet, with slow connections, in an external field; it is suitable for undifferentiated-participant scenarios. In differentiatedparticipant scenarios, untying parameters results in an infinite-range spin glass whose degrees of freedom scale as the square of the number of participants; it offers an efficient representation of participant-pair synchrony. We discuss the implications of model parametrization and of the thermodynamic and feed-forward perceptron formalisms for easily quantifying aspects of conversational dynamics.
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