Abstract- When phylogeneticists choose among alternative hypotheses, they choose the one that requires the fewest ad hoc assumptions, i.e. the one that is the most parsimonious. For some systematists, choosing among alternative transformation series for the same set of taxa is equivalent to attaining trees with shorter length and minimal homoplasy. Homoplasy is shown to be composed of hierarchical discordance and scattering, which are recognized and described for the first time. Neither the consistency nor retention indices can be used in assessing different theories of multistate character transformation because both are affected by the shape of the transformation series rather than the character state distribution on a tree. Fits of transformations to a tree are better assessed by comparing the transformation to the cladogram character and the nearest neighbor network. Nearest neighbor networks are graphical representations of the nearest neighbor matrix. Transformations with the closest greatest number of matches between cladogram characters and the least complexity in the nearest neighbor network are preferred. These transformations are shown to make the fewest number of ad hoc statements and hence to be the most parsimonious. A means for obtaining cladogram characters and nearest neighbor matrices using a widely distributed microcomputer program is presented.