There has existed since the 1930s a dichotomy among practitioners in the field regarding the electrostatic interactions in colloidal suspensions and polyelectrolyte solutions, viz., whether the electrical free energy is attractive or repulsive. The well-known Derjaguin-Landau-Verwey-Overbeek (DLVO) theory views the electrostatic interactions between a pair of charged macroparticles as a repulsive interaction, whereas the many-bodied "salt-crystal" structure of colloidal suspensions of Langmuir gives rise to a net attractive electrostatic interaction. Experimental data Likewise are not definitive regarding these two apparently opposite points of view on the role of electrostatic interactions in these complex systems. For example, recent digital video studies by Grier and co-workers on polystyrene latex spheres (PLS) indicate that the pairwise interaction potential is repulsive and of the Yukawa form, whereas a collection of PLS particles has a long-range attractive component. A method is described herein based on a chemical model and the juxtaposition of potential fields (JPF) for multibody interaction systems. The JPF method is based on a topological procedure for identifying chemical bonding in molecules by vector gradient mapping. Vector gradient mapping methods applied to the JPF method indicate the importance of the distribution of counterions in determining the stability of a system of highly charged spheres. It is this distribution of the counterions in response to the potential fields of the macroions that provides a "crossover" from a repulsive interaction between two isolated spheres (unstable structure) to an attractive interaction for a group of spheres (stable cluster). Salient features of the JPF approach to charged colloidal systems are that it (1) does not rely on a particular form of the interaction potential, (2) identifies the shortcoming of the pair potential in the describing many-body effects, and (3) provides three mechanisms for the stability of clusters of macroions of like charge.