In this paper, we closely examine the various ways in which a multi-party argumentative discussion—argumentative polylogue—can be analyzed in a dialectical framework. Our chief concern is that while multi-party and multi-position discussions are characteristic of a large class of argumentative activities, dialectical approaches would analyze and evaluate them in terms of dyadic exchanges between two parties: pro and con. Using as an example an academic committee arguing about the researcher of the year as well as other cases from argumentation literature, (...) we scrutinize the advantages and pitfalls of applying a dialectical framework to polylogue analysis and evaluation. We recognize two basic dialectical methods: interpreting polylogues as exchanges between two main camps and splitting polylogues into a multitude of dual encounters. On the basis of this critical inquiry, we lay out an argument expressing the need for an improved polylogical model and propose its basic elements. (shrink)