Comparing and contrasting the uses of two graphical tools for displaying patterns of multiparty competition: Nagayama diagrams and simplex representations

We compare two tools for displaying, in graphical form, information about vote outcomes in multiparty elections at the constituency level. One was recently proposed by Nagayama and introduced to the English-speaking world by Reed, who applied this method to Japanese and Italian election data. Reed labels the method Nagayama diagrams. Recently, Taagepera has shown how the domain of potential uses of Nagayama diagrams can be expanded significantly. A second graphical device has been used by a number of authors for various types of election analyses, but is not that well known in the comparative parties literature. This method, which uses barycentric coordinates (i.e. triangular) rather than the more familiar rectangular coordinates, has gone under a variety of names (e.g. trilinear plot, toroidal diagram and simplex representation), but we have chosen to use the last of these labels. We make use of both methods to visually present election data (by constituency) for the Italian national elections of 1994, 1996 and 2001. We show how different types of information may be readily gleaned from the two types of graph, and, perhaps most importantly, illustrate how we may improve the ready intuitive interpretability of each type of graph by specifying boundary constraints to define particular regions of the graph - a technique we call 'segmentation'.