The taking of turns to speak is an intrinsic property of conversation. It is expected that models of taking turns, providing a prior distribution over conversational form, can reduce the perplexity of what is attended to and processed by spoken dialogue systems. We propose a single-port model of multi-party turn-taking which allows conversants to behave independently but to condition their behavior on the past of the entire group. The model performs at least as well as an existing multi-port model on perplexity over subsequent speech activity. We quantify the effect of longer histories and more distant future horizons, and argue that the framework has the potential to inform the design and behavior of spoken dialogue systems.