In this paper, we study the effect of a simple majority rule on two classes of chordal rings: weakly and strongly chorded rings. In the case of weakly chorded rings, we establish a lower bound on the weight of optimal dynamos and we prove that the bound is tight with a constructive upper bound; we also provide a complete characterization of the optimal dynamos for the well-known class of double- and triple-loop networks. Also in the case of strongly chorded rings, we establish tight bounds and show how to construct optimal dynamos.
